Log in

Relevant bibliographies by topics / Hilbert schemes of points on K3 surface / Journal articles

Journal articles on the topic 'Hilbert schemes of points on K3 surface'

To see the other types of publications on this topic, follow the link: Hilbert schemes of points on K3 surface.

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Hilbert schemes of points on K3 surface.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Charles, François, and Eyal Markman. "The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces." Compositio Mathematica 149, no. 3 (February 7, 2013): 481–94. http://dx.doi.org/10.1112/s0010437x12000607.

Full text

Abstract:

AbstractWe prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic sheaves and a study of the cohomology algebra of Hilbert schemes of K3 surfaces.

APA, Harvard, Vancouver, ISO, and other styles

2

Ryan, Tim, and Ruijie Yang. "Nef Cones of Nested Hilbert Schemes of Points on Surfaces." International Mathematics Research Notices 2020, no. 11 (May 28, 2018): 3260–94. http://dx.doi.org/10.1093/imrn/rny088.

Full text

Abstract:

Abstract Let X be the projective plane, a Hirzebruch surface, or a general K3 surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on X. We calculate the nef cone for two types of nested Hilbert schemes. As an application, we recover a theorem of Butler on syzygies on Hirzebruch surfaces.

APA, Harvard, Vancouver, ISO, and other styles

3

Bruzzo, Ugo, and Antony Maciocia. "Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 2 (August 1996): 255–61. http://dx.doi.org/10.1017/s0305004100074843.

Full text

Abstract:

AbstractBy using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces X the Hilbert schemes Hilbn(X) can be identified for all n ≥ 1 with moduli spaces of Gieseker stable vector bundles on X. We also introduce a new Fourier-Mukai type transform for such surfaces.

APA, Harvard, Vancouver, ISO, and other styles

4

Cattaneo, Alberto. "Automorphisms of Hilbert schemes of points on a generic projective K3 surface." Mathematische Nachrichten 292, no. 10 (July 26, 2019): 2137–52. http://dx.doi.org/10.1002/mana.201800557.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Sawon, Justin. "Lagrangian fibrations on Hilbert schemes of points on K3 surfaces." Journal of Algebraic Geometry 16, no. 3 (September 1, 2007): 477–97. http://dx.doi.org/10.1090/s1056-3911-06-00453-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Kapfer, Simon. "Computing cup products in integral cohomology of Hilbert schemes of points on K3 surfaces." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 78–97. http://dx.doi.org/10.1112/s1461157016000012.

Full text

Abstract:

We study cup products in the integral cohomology of the Hilbert scheme of $n$ points on a K3 surface and present a computer program for this purpose. In particular, we deal with the question of which classes can be represented by products of lower degrees.Supplementary materials are available with this article.

APA, Harvard, Vancouver, ISO, and other styles

7

Oberdieck, Georg. "Gromov–Witten invariants of the Hilbert schemes of points of a K3 surface." Geometry & Topology 22, no. 1 (October 31, 2017): 323–437. http://dx.doi.org/10.2140/gt.2018.22.323.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Bangere, Purnaprajna, Jayan Mukherjee, and Debaditya Raychaudhury. "K3 carpets on minimal rational surfaces and their smoothings." International Journal of Mathematics 32, no. 06 (April 7, 2021): 2150032. http://dx.doi.org/10.1142/s0129167x21500324.

Full text

Abstract:

In this paper, we study K3 double structures on minimal rational surfaces [Formula: see text]. The results show there are infinitely many non-split abstract K3 double structures on [Formula: see text] parametrized by [Formula: see text], countably many of which are projective. For [Formula: see text] there exists a unique non-split abstract K3 double structure which is non-projective (see [J.-M. Drézet, Primitive multiple schemes, preprint (2020), arXiv:2004.04921, to appear in Eur. J. Math.]). We show that all projective K3 carpets can be smoothed to a smooth K3 surface. One of the byproducts of the proof shows that unless [Formula: see text] is embedded as a variety of minimal degree, there are infinitely many embedded K3 carpet structures on [Formula: see text]. Moreover, we show any embedded projective K3 carpet on [Formula: see text] with [Formula: see text] arises as a flat limit of embeddings degenerating to 2:1 morphism. The rest do not, but we still prove the smoothing result. We further show that the Hilbert points corresponding to the projective K3 carpets supported on [Formula: see text], embedded by a complete linear series are smooth points if and only if [Formula: see text]. In contrast, Hilbert points corresponding to projective (split) K3 carpets supported on [Formula: see text] and embedded by a complete linear series are always smooth. The results in [P. Bangere, F. J. Gallego and M. González, Deformations of hyperelliptic and generalized hyperelliptic polarized varieties, preprint (2020), arXiv:2005.00342] show that there are no higher dimensional analogues of the results in this paper.

APA, Harvard, Vancouver, ISO, and other styles

9

Neguţ, Andrei, Georg Oberdieck, and Qizheng Yin. "Motivic decompositions for the Hilbert scheme of points of a K3 surface." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 778 (April 19, 2021): 65–95. http://dx.doi.org/10.1515/crelle-2021-0015.

Full text

Abstract:

Abstract We construct an explicit, multiplicative Chow–Künneth decomposition for the Hilbert scheme of points of a K3 surface. We further refine this decomposition with respect to the action of the Looijenga–Lunts–Verbitsky Lie algebra.

APA, Harvard, Vancouver, ISO, and other styles

10

Reede, Fabian, and Ziyu Zhang. "Stability of some vector bundles on Hilbert schemes of points on K3 surfaces." Mathematische Zeitschrift 301, no. 1 (December 3, 2021): 315–41. http://dx.doi.org/10.1007/s00209-021-02920-6.

Full text

Abstract:

AbstractLet X be a projective K3 surfaces. In two examples where there exists a fine moduli space M of stable vector bundles on X, isomorphic to a Hilbert scheme of points, we prove that the universal family $${\mathcal {E}}$$ E on $$X\times M$$ X × M can be understood as a complete flat family of stable vector bundles on M parametrized by X, which identifies X with a smooth connected component of some moduli space of stable sheaves on M.

APA, Harvard, Vancouver, ISO, and other styles

11

Meachan, Ciaran, Giovanni Mongardi, and Kōta Yoshioka. "Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational." Mathematische Zeitschrift 294, no. 3-4 (April 2, 2019): 871–80. http://dx.doi.org/10.1007/s00209-019-02281-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Verbitsky, M. "Trianalytic Subvarieties of the Hilbert Scheme of Points on a K3 Surface." Geometric And Functional Analysis 8, no. 4 (September 1, 1998): 732–82. http://dx.doi.org/10.1007/s000390050072.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Manschot, Jan, and Jose Miguel Zapata Rolon. "The asymptotic profile of $\chi_y$-genera of Hilbert schemes of points on K3 surfaces." Communications in Number Theory and Physics 9, no. 2 (2015): 413–35. http://dx.doi.org/10.4310/cntp.2015.v9.n2.a6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Iliev, Atanas, Grzegorz Kapustka, Michał Kapustka, and Kristian Ranestad. "EPW cubes." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 748 (March 1, 2019): 241–68. http://dx.doi.org/10.1515/crelle-2016-0044.

Full text

Abstract:

Abstract We construct a new 20-dimensional family of projective six-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 surface and are constructed as natural double covers of special codimension-three subvarieties of the Grassmannian G(3,6) . These codimension-three subvarieties are defined as Lagrangian degeneracy loci and their construction is parallel to that of EPW sextics, we call them the EPW cubes. As a consequence we prove that the moduli space of polarized IHS sixfolds of K3 -type, Beauville–Bogomolov degree 4 and divisibility 2 is unirational.

APA, Harvard, Vancouver, ISO, and other styles

15

Bakker, Benjamin. "A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES." Journal of the Institute of Mathematics of Jussieu 16, no. 4 (September 9, 2015): 859–77. http://dx.doi.org/10.1017/s1474748015000328.

Full text

Abstract:

Classically, an indecomposable class $R$ in the cone of effective curves on a K3 surface $X$ is representable by a smooth rational curve if and only if $R^{2}=-2$. We prove a higher-dimensional generalization conjectured by Hassett and Tschinkel: for a holomorphic symplectic variety $M$ deformation equivalent to a Hilbert scheme of $n$ points on a K3 surface, an extremal curve class $R\in H_{2}(M,\mathbb{Z})$ in the Mori cone is the line in a Lagrangian $n$-plane $\mathbb{P}^{n}\subset M$ if and only if certain intersection-theoretic criteria are met. In particular, any such class satisfies $(R,R)=-\frac{n+3}{2}$, and the primitive such classes are all contained in a single monodromy orbit.

APA, Harvard, Vancouver, ISO, and other styles

16

Nieper-Wißkirchen, Marc A. "Calculation of Rozansky-Witten invariants on the Hilbert schemes of points on a K3 surface and the generalised kummer varieties." Documenta Mathematica 8 (2003): 591–623. http://dx.doi.org/10.4171/dm/153.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Laterveer, Robert. "Algebraic cycles and Lehn–Lehn–Sorger–van Straten eightfolds." Proceedings of the Edinburgh Mathematical Society 64, no. 4 (October 4, 2021): 884–907. http://dx.doi.org/10.1017/s001309152100064x.

Full text

Abstract:

AbstractThis article is about Lehn–Lehn–Sorger–van Straten eightfolds $Z$ and their anti-symplectic involution $\iota$. When $Z$ is birational to the Hilbert scheme of points on a K3 surface, we give an explicit formula for the action of $\iota$ on the Chow group of $0$-cycles of $Z$. The formula is in agreement with the Bloch–Beilinson conjectures and has some non-trivial consequences for the Chow ring of the quotient.

APA, Harvard, Vancouver, ISO, and other styles

18

Oberdieck, Georg. "Gromov–Witten Theory of $\text{K3} \times {\mathbb{P}}^1$ and Quasi-Jacobi Forms." International Mathematics Research Notices 2019, no. 16 (November 2, 2017): 4966–5011. http://dx.doi.org/10.1093/imrn/rnx267.

Full text

Abstract:

Abstract Let $S$ be a K3 surface with primitive curve class $\beta$. We solve the relative Gromov–Witten theory of $S \times {\mathbb{P}}^1$ in classes $(\beta,1)$ and $(\beta,2)$. The generating series are quasi-Jacobi forms and equal to a corresponding series of genus $0$ Gromov–Witten invariants on the Hilbert scheme of points of $S$. This proves a special case of a conjecture of Pandharipande and the author. The new geometric input of the paper is a genus bound for hyperelliptic curves on K3 surfaces proven by Ciliberto and Knutsen. By exploiting various formal properties we find that a key generating series is determined by the very first few coefficients. Let $E$ be an elliptic curve. As collorary of our computations, we prove that Gromov–Witten invariants of $S \times E$ in classes $(\beta,1)$ and $(\beta,2)$ are coefficients of the reciprocal of the Igusa cusp form. We also calculate several linear Hodge integrals on the moduli space of stable maps to a K3 surface and the Gromov–Witten invariants of an abelian threefold in classes of type $(1,1,d)$.

APA, Harvard, Vancouver, ISO, and other styles

19

Oberdieck, Georg. "A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface." Commentarii Mathematici Helvetici 96, no. 1 (March 12, 2021): 65–77. http://dx.doi.org/10.4171/cmh/507.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Camere, Chiara, Alice Garbagnati, and Giovanni Mongardi. "Calabi–Yau Quotients of Hyperkähler Four-folds." Canadian Journal of Mathematics 71, no. 1 (February 2019): 45–92. http://dx.doi.org/10.4153/cjm-2018-025-1.

Full text

Abstract:

AbstractThe aim of this paper is to construct Calabi–Yau 4-folds as crepant resolutions of the quotients of a hyperkähler 4-fold $X$ by a non-symplectic involution $\unicode[STIX]{x1D6FC}$. We first compute the Hodge numbers of a Calabi–Yau constructed in this way in a general setting, and then we apply the results to several specific examples of non-symplectic involutions, producing Calabi–Yau 4-folds with different Hodge diamonds. Then we restrict ourselves to the case where $X$ is the Hilbert scheme of two points on a K3 surface $S$, and the involution $\unicode[STIX]{x1D6FC}$ is induced by a non-symplectic involution on the K3 surface. In this case we compare the Calabi–Yau 4-fold $Y_{S}$, which is the crepant resolution of $X/\unicode[STIX]{x1D6FC}$, with the Calabi–Yau 4-fold $Z_{S}$, constructed from $S$ through the Borcea–Voisin construction. We give several explicit geometrical examples of both these Calabi–Yau 4-folds, describing maps related to interesting linear systems as well as a rational $2:1$ map from $Z_{S}$ to $Y_{S}$.

APA, Harvard, Vancouver, ISO, and other styles

21

Markman, Eyal. "Stability of a natural sheaf over the cartesian square of the Hilbert scheme of points on a K3 surface." Mathematische Zeitschrift 287, no. 3-4 (February 21, 2017): 985–92. http://dx.doi.org/10.1007/s00209-017-1855-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Biswas, Indranil, and Avijit Mukherjee. "On the symplectic structures on moduli space of stable sheaves over a K3 or abelian surface and on Hilbert scheme of points." Archiv der Mathematik 80, no. 5 (May 1, 2003): 507–15. http://dx.doi.org/10.1007/s00013-003-4613-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Amerik, Ekaterina. "On an automorphism of Hilb[2] of certain K3 surfaces." Proceedings of the Edinburgh Mathematical Society 54, no. 1 (January 19, 2011): 1–7. http://dx.doi.org/10.1017/s0013091509001138.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Gyenge, Ádám, András Némethi, and Balázs Szendrői. "Euler characteristics of Hilbert schemes of points on simple surface singularities." European Journal of Mathematics 4, no. 2 (March 26, 2018): 439–524. http://dx.doi.org/10.1007/s40879-018-0222-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Donin, Niccolò Lora Lamia. "Transverse Hilbert schemes and completely integrable systems." Complex Manifolds 4, no. 1 (December 20, 2017): 263–72. http://dx.doi.org/10.1515/coma-2017-0015.

Full text

Abstract:

Abstract In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

APA, Harvard, Vancouver, ISO, and other styles

26

Ran, Ziv. "Incidence stratifications on Hilbert schemes of smooth surfaces, and an application to Poisson structures." International Journal of Mathematics 27, no. 01 (January 2016): 1650006. http://dx.doi.org/10.1142/s0129167x16500063.

Full text

Abstract:

Given a smooth curve on a smooth surface, the Hilbert scheme of points on the surface is stratified according to the length of the intersection with the curve. The strata are highly singular. We show that this stratification admits a natural log-resolution, namely the stratified blowup. As a consequence, the induced Poisson structure on the Hilbert scheme of a Poisson surface has unobstructed deformations.

APA, Harvard, Vancouver, ISO, and other styles

27

Song, Lei. "On the universal family of Hilbert schemes of points on a surface." Journal of Algebra 456 (June 2016): 348–54. http://dx.doi.org/10.1016/j.jalgebra.2016.03.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Gholampour, Amin, and Richard P. Thomas. "Degeneracy loci, virtual cycles and nested Hilbert schemes II." Compositio Mathematica 156, no. 8 (August 2020): 1623–63. http://dx.doi.org/10.1112/s0010437x20007290.

Full text

Abstract:

We express nested Hilbert schemes of points and curves on a smooth projective surface as ‘virtual resolutions’ of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories to produce the virtual cycles of Vafa–Witten theory and other sheaf-counting problems. The result is an effective way of calculating invariants (VW, SW, local PT and local DT) via Thom–Porteous-like Chern class formulae.

APA, Harvard, Vancouver, ISO, and other styles

29

Boissière, Samuel, and Marc A. Nieper-Wisskirchen. "Generating Series in the Cohomology of Hilbert Schemes of Points on Surfaces." LMS Journal of Computation and Mathematics 10 (2007): 254–70. http://dx.doi.org/10.1112/s146115700000139x.

Full text

Abstract:

In the study of the rational cohomology of Hilbert schemes of points on a smooth surface, it is particularly interesting to understand the characteristic classes of the tautological bundles and the tangent bundle. In this note we pursue this study. We first collect all results appearing separately in the literature and prove some new formulas using Ohmoto's results on orbifold Chern classes on Hilbert schemes. We also explain the algorithmic counterpart of the topic: the cohomology space is governed by a vertex algebra that can be used to compute characteristic classes. We present an implementation of the vertex operators in the rewriting logic system MAUDE, and address observations and conjectures obtained after symbolic computations.

APA, Harvard, Vancouver, ISO, and other styles

30

Scala, Luca. "Some remarks on tautological sheaves on Hilbert schemes of points on a surface." Geometriae Dedicata 139, no. 1 (December 2, 2008): 313–29. http://dx.doi.org/10.1007/s10711-008-9338-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Bottacin, F. "Poisson structures on Hilbert schemes of points¶of a surface and integrable systems." manuscripta mathematica 97, no. 4 (December 1, 1998): 517–27. http://dx.doi.org/10.1007/s002290050118.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Paul, Arjun, and Ronnie Sebastian. "Fundamental group schemes of Hilbert scheme of n points on a smooth projective surface." Bulletin des Sciences Mathématiques 164 (November 2020): 102898. http://dx.doi.org/10.1016/j.bulsci.2020.102898.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Hu, Jianxun, Wei-Ping Li, and Zhenbo Qin. "The Gromov–Witten invariants of the Hilbert schemes of points on surfaces with pg > 0." International Journal of Mathematics 26, no. 01 (January 2015): 1550009. http://dx.doi.org/10.1142/s0129167x15500093.

Full text

Abstract:

In this paper, we study the Gromov–Witten theory of the Hilbert schemes X[n] of points on a smooth projective surface X with positive geometric genus pg. For fixed distinct points x1, …, xn-1 ∈ X, let βn be the homology class of the curve {ξ + x2 + ⋯ + xn-1 ∈ X[n] | Supp (ξ) = {x1}}, and let βKX be the homology class of {x + x1 + ⋯ + xn-1 ∈ X[n] | x ∈ KX}. Using cosection localization technique due to Y. Kiem and J. Li, we prove that if X is a simply connected surface admitting a holomorphic differential two-form with irreducible zero divisor, then all the Gromov–Witten invariants of X[n] defined via the moduli space [Formula: see text] of stable maps vanish except possibly when β is a linear combination of βn and βKX. When n = 2, the exceptional cases can be further reduced to the Gromov–Witten invariants: [Formula: see text] with [Formula: see text] and d ≤ 3, and [Formula: see text] with d ≥ 1. When [Formula: see text], we show that [Formula: see text] which is consistent with a well-known formula of C. Taubes. In addition, for an arbitrary surface X and d ≥ 1, we verify that [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

34

Hayashi, Taro. "Automorphisms of the Hilbert schemes of n points of a rational surface and the anticanonical Iitaka dimension." Geometriae Dedicata 207, no. 1 (January 8, 2020): 395–407. http://dx.doi.org/10.1007/s10711-019-00504-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Henni, Abdelmoubine A., and Douglas M. Guimarães. "A note on the ADHM description of Quot schemes of points on affine spaces." International Journal of Mathematics 32, no. 06 (March 18, 2021): 2150031. http://dx.doi.org/10.1142/s0129167x21500312.

Full text

Abstract:

We give an Atiyah–Drinfel’d–Hitchin–Manin (ADHM) description of the Quot scheme of points [Formula: see text] of length [Formula: see text] and rank [Formula: see text] on affine spaces [Formula: see text] which naturally extends both Baranovsky’s representation of the punctual Quot scheme on a smooth surface and the Hilbert scheme of points on affine spaces [Formula: see text] described by the first author and M. Jardim. Using results on the variety of commuting matrices, and combining them with our construction, we prove new properties concerning irreducibility and reducedness of [Formula: see text] and its punctual version [Formula: see text] where [Formula: see text] is a fixed point on a smooth affine variety [Formula: see text]. In this last case, we also study a connectedness result, for some special cases of higher [Formula: see text] and [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

36

RYAN, TIM. "THE EFFECTIVE CONE OF MODULI SPACES OF SHEAVES ON A SMOOTH QUADRIC SURFACE." Nagoya Mathematical Journal 232 (September 4, 2017): 151–215. http://dx.doi.org/10.1017/nmj.2017.24.

Full text

Abstract:

Let $\unicode[STIX]{x1D709}$ be a stable Chern character on $\mathbb{P}^{1}\times \mathbb{P}^{1}$, and let $M(\unicode[STIX]{x1D709})$ be the moduli space of Gieseker semistable sheaves on $\mathbb{P}^{1}\times \mathbb{P}^{1}$ with Chern character $\unicode[STIX]{x1D709}$. In this paper, we provide an approach to computing the effective cone of $M(\unicode[STIX]{x1D709})$. We find Brill–Noether divisors spanning extremal rays of the effective cone using resolutions of the general elements of $M(\unicode[STIX]{x1D709})$ which are found using the machinery of exceptional bundles. We use this approach to provide many examples of extremal rays in these effective cones. In particular, we completely compute the effective cone of the first fifteen Hilbert schemes of points on $\mathbb{P}^{1}\times \mathbb{P}^{1}$.

APA, Harvard, Vancouver, ISO, and other styles

37

Zhan, Sailun. "Counting Rational Curves on K3 Surfaces With Finite Group Actions." International Mathematics Research Notices, January 4, 2021. http://dx.doi.org/10.1093/imrn/rnaa320.

Full text

Abstract:

Abstract Göttsche gave a formula for the dimension of the cohomology of Hilbert schemes of points on a smooth projective surface $S$. When $S$ admits an action by a finite group $G$, we describe the action of $G$ on the Hodge structure. In the case that $S$ is a K3 surface, each element of $G$ gives a trace on $\sum _{n=0}^{\infty }\sum _{i=0}^{\infty }(-1)^{i}H^{i}(S^{[n]},\mathbb{C})q^{n}$. When $G$ acts faithfully and symplectically on $S$, the resulting generating function is of the form $q/f(q)$, where $f(q)$ is a cusp form. We relate the Hodge structure of Hilbert schemes of points to the Hodge structure of the compactified Jacobian of the tautological family of curves over an integral linear system on a K3 surface as $G$-representations. Finally, we give a sufficient condition for a $G$-orbit of curves with nodal singularities not to contribute to the representation.

APA, Harvard, Vancouver, ISO, and other styles

38

Beri, Pietro, and Alberto Cattaneo. "On birational transformations of Hilbert schemes of points on K3 surfaces." Mathematische Zeitschrift, January 20, 2022. http://dx.doi.org/10.1007/s00209-021-02960-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

CAMERE, CHIARA, ALBERTO CATTANEO, and ANDREA CATTANEO. "NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF -TYPE." Nagoya Mathematical Journal, February 27, 2020, 1–25. http://dx.doi.org/10.1017/nmj.2019.43.

Full text

Abstract:

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all $d$ -dimensional families of manifolds of $K3^{[n]}$ -type with a non-symplectic involution for $d\geqslant 19$ and $n\leqslant 5$ and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.

APA, Harvard, Vancouver, ISO, and other styles

40

Göttsche, Lothar. "Refined Verlinde formulas for Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces." Épijournal de Géométrie Algébrique Volume 4 (October 9, 2020). http://dx.doi.org/10.46298/epiga.2020.volume4.5282.

Full text

Abstract:

We compute generating functions for elliptic genera with values in line bundles on Hilbert schemes of points on surfaces. As an application we also compute generating functions for elliptic genera with values in determinant line bundles on moduli spaces of sheaves on K3 surfaces.

APA, Harvard, Vancouver, ISO, and other styles

41

Ouchi, Genki. "Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds." Communications in Algebra, November 5, 2020, 1–7. http://dx.doi.org/10.1080/00927872.2020.1829636.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Bakker, Benjamin, and Andrei Jorza. "Lagrangian 4-planes in holomorphic symplectic varieties of K3[4]-type." Open Mathematics 12, no. 7 (January 1, 2014). http://dx.doi.org/10.2478/s11533-013-0389-3.

Full text

Abstract:

AbstractWe classify the cohomology classes of Lagrangian 4-planes ℙ4 in a smooth manifold X deformation equivalent to a Hilbert scheme of four points on a K3 surface, up to the monodromy action. Classically, the Mori cone of effective curves on a K3 surface S is generated by nonnegative classes C, for which (C, C) ≥ 0, and nodal classes C, for which (C, C) = −2; Hassett and Tschinkel conjecture that the Mori cone of a holomorphic symplectic variety X is similarly controlled by “nodal” classes C such that (C, C) = −γ, for (·,·) now the Beauville-Bogomolov form, where γ classifies the geometry of the extremal contraction associated to C. In particular, they conjecture that for X deformation equivalent to a Hilbert scheme of n points on a K3 surface, the class C = ℓ of a line in a smooth Lagrangian n-plane ℙn must satisfy (ℓ,ℓ) = −(n + 3)/2. We prove the conjecture for n = 4 by computing the ring of monodromy invariants on X, and showing there is a unique monodromy orbit of Lagrangian 4-planes.

APA, Harvard, Vancouver, ISO, and other styles

43

Maulik, Davesh, and Andrei Neguţ. "LEHN’S FORMULA IN CHOW AND CONJECTURES OF BEAUVILLE AND VOISIN." Journal of the Institute of Mathematics of Jussieu, August 3, 2020, 1–39. http://dx.doi.org/10.1017/s1474748020000377.

Full text

Abstract:

The Beauville–Voisin conjecture for a hyperkähler manifold $X$ states that the subring of the Chow ring $A^{\ast }(X)$ generated by divisor classes and Chern characters of the tangent bundle injects into the cohomology ring of $X$ . We prove a weak version of this conjecture when $X$ is the Hilbert scheme of points on a K3 surface for the subring generated by divisor classes and tautological classes. This in particular implies the weak splitting conjecture of Beauville for these geometries. In the process, we extend Lehn’s formula and the Li–Qin–Wang $W_{1+\infty }$ algebra action from cohomology to Chow groups for the Hilbert scheme of an arbitrary smooth projective surface $S$ .

APA, Harvard, Vancouver, ISO, and other styles

44

Bini, Gilberto, Samuel Boissière, and Flaminio Flamini. "Some families of big and stable bundles on K3 surfaces and on their Hilbert schemes of points." manuscripta mathematica, November 12, 2022. http://dx.doi.org/10.1007/s00229-022-01439-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Kretschmer, Andreas. "The Chow ring of hyperkähler varieties of $$K3^{[2]}$$-type via Lefschetz actions." Mathematische Zeitschrift, September 9, 2021. http://dx.doi.org/10.1007/s00209-021-02846-z.

Full text

Abstract:

AbstractWe propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of $$K3^{[2]}$$ K 3 [ 2 ] -type to the Chow ring of correspondences $$\mathrm{CH}^*(X \times X)$$ CH ∗ ( X × X ) in terms of a canonical lift of the Beauville–Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a K3 surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of X of Shen and Vial agrees with the eigenspace decomposition of a canonical lift of the cohomological grading operator.

APA, Harvard, Vancouver, ISO, and other styles

46

Menet, Grégoire. "Integral cohomology of quotients via toric geometry." Épijournal de Géométrie Algébrique Volume 6 (February 23, 2022). http://dx.doi.org/10.46298/epiga.2022.volume6.5762.

Full text

Abstract:

We describe the integral cohomology of $X/G$ where $X$ is a compact complex manifold and $G$ a cyclic group of prime order with only isolated fixed points. As a preliminary step, we investigate the integral cohomology of toric blow-ups of quotients of $\mathbb{C}^n$. We also provide necessary and sufficient conditions for the spectral sequence of equivariant cohomology of $(X,G)$ to degenerate at the second page. As an application, we compute the Beauville--Bogomolov form of $X/G$ when $X$ is a Hilbert scheme of points on a K3 surface and $G$ a symplectic automorphism group of orders 5 or 7.

APA, Harvard, Vancouver, ISO, and other styles

47

Floccari, Salvatore. "On the Mumford–Tate conjecture for hyperkähler varieties." manuscripta mathematica, May 25, 2021. http://dx.doi.org/10.1007/s00229-021-01316-4.

Full text

Abstract:

AbstractWe study the Mumford–Tate conjecture for hyperkähler varieties. We show that the full conjecture holds for all varieties deformation equivalent to either an Hilbert scheme of points on a K3 surface or to O’Grady’s ten dimensional example, and all of their self-products. For an arbitrary hyperkähler variety whose second Betti number is not 3, we prove the Mumford–Tate conjecture in every codimension under the assumption that the Künneth components in even degree of its André motive are abelian. Our results extend a theorem of André.

APA, Harvard, Vancouver, ISO, and other styles

48

Rieß, Ulrike. "On the non-divisorial base locus of big and nef line bundles on K3[2]-type varieties." Proceedings of the Royal Society of Edinburgh: Section A Mathematics, February 20, 2020, 1–27. http://dx.doi.org/10.1017/prm.2020.2.

Full text

Abstract:

Abstract We approach non-divisorial base loci of big and nef line bundles on irreducible symplectic varieties. While for K3 surfaces, only divisorial base loci can occur, nothing was known about the behaviour of non-divisorial base loci for more general irreducible symplectic varieties. We determine the base loci of all big and nef line bundles on the Hilbert scheme of two points on very general K3 surfaces of genus two and on their birational models. Remarkably, we find an ample line bundle with a non-trivial base locus in codimension two. We deduce that, generically in the moduli spaces of polarized K3[2]-type varieties, the polarization is base point free.

APA, Harvard, Vancouver, ISO, and other styles

49

Jin, Seokho, and Sihun Jo. "On the algebraicity about the Hodge numbers of the Hilbert schemes of algebraic surfaces." Proceedings of the Edinburgh Mathematical Society, April 19, 2022, 1–12. http://dx.doi.org/10.1017/s0013091522000141.

Full text

Abstract:

Abstract Hilbert schemes are an object arising from geometry and are closely related to physics and modular forms. Recently, there have been investigations from number theorists about the Betti numbers and Hodge numbers of the Hilbert schemes of points of an algebraic surface. In this paper, we prove that Göttsche's generating function of the Hodge numbers of Hilbert schemes of $n$ points of an algebraic surface is algebraic at a CM point $\tau$ and rational numbers $z_1$ and $z_2$ . Our result gives a refinement of the algebraicity on Betti numbers.

APA, Harvard, Vancouver, ISO, and other styles

50

BRAKKEE, EMMA. "Two polarised K3 surfaces associated to the same cubic fourfold." Mathematical Proceedings of the Cambridge Philosophical Society, March 16, 2020, 1–14. http://dx.doi.org/10.1017/s0305004120000055.

Full text

Abstract:

Abstract For infinitely many d, Hassett showed that special cubic fourfolds of discriminant d are related to polarised K3 surfaces of degree d via their Hodge structures. For half of the d, each associated K3 surface (S, L) canonically yields another one, (Sτ, Lτ). We prove that Sτ is isomorphic to the moduli space of stable coherent sheaves on S with Mukai vector (3, L, d/6). We also explain for which d the Hilbert schemes Hilb n (S) and Hilb n (Sτ) are birational.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!