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Journal articles on the topic 'Semistable sheaves'

Author: Grafiati

Published: 14 March 2023

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1

Bertram, Aaron, and Cristian Martinez. "Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing." International Mathematics Research Notices 2020, no. 7 (April 25, 2018): 2007–33. http://dx.doi.org/10.1093/imrn/rny065.

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Abstract We prove that the “Thaddeus flips” of L-twisted sheaves constructed by Matsuki and Wentworth explaining the change of polarization for Gieseker semistable sheaves on a surface can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of one-dimensional Gieseker semistable sheaves on a surface by varying a family of stability conditions.

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2

Choi, Jinwon, and Kiryong Chung. "Cohomology bounds for sheaves of dimension one." International Journal of Mathematics 25, no. 11 (October 2014): 1450103. http://dx.doi.org/10.1142/s0129167x14501031.

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We find sharp bounds on h0(F) for one-dimensional semistable sheaves F on a projective variety X. When X is the projective plane ℙ2, we study the stratification of the moduli space by the spectrum of sheaves. We show that the deepest stratum is isomorphic to a closed subset of a relative Hilbert scheme. This provides an example of a family of semistable sheaves having the biggest dimensional global section space.

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3

Langer, Adrian. "Semistable sheaves in positive characteristic." Annals of Mathematics 159, no. 1 (January 1, 2004): 251–76. http://dx.doi.org/10.4007/annals.2004.159.251.

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4

Langer, Adrian. "On boundedness of semistable sheaves." Documenta Mathematica 27 (2022): 1–16. http://dx.doi.org/10.4171/dm/865.

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5

Andreatta, Fabrizio, and Adrian Iovita. "Semistable Sheaves and Comparison Isomorphisms in the Semistable Case." Rendiconti del Seminario Matematico della Università di Padova 128 (2012): 131–285. http://dx.doi.org/10.4171/rsmup/128-7.

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6

Patel, Deepam, Tobias Schmidt, and Matthias Strauch. "LOCALLY ANALYTIC REPRESENTATIONS OF VIA SEMISTABLE MODELS OF." Journal of the Institute of Mathematics of Jussieu 18, no. 1 (January 12, 2017): 125–87. http://dx.doi.org/10.1017/s1474748016000396.

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In this paper we study certain sheaves of $p$-adically complete rings of differential operators on semistable models of the projective line over the ring of integers in a finite extension $L$ of $\mathbb{Q}_{p}$. The global sections of these sheaves can be identified with (central reductions of) analytic distribution algebras of wide open congruence subgroups. It is shown that the global sections functor furnishes an equivalence between the categories of coherent module sheaves and finitely presented modules over the distribution algebras. Using the work of M. Emerton, we then describe admissible representations of $\text{GL}_{2}(L)$ in terms of sheaves on the projective limit of these formal schemes. As an application, we show that representations coming from certain equivariant line bundles on Drinfeld’s first étale covering of the $p$-adic upper half plane are admissible.

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7

ABE, TAKESHI. "SEMISTABLE SHEAVES WITH SYMMETRIC ON A QUADRIC SURFACE." Nagoya Mathematical Journal 227 (October 5, 2016): 86–159. http://dx.doi.org/10.1017/nmj.2016.50.

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For moduli spaces of sheaves with symmetric $c_{1}$ on a quadric surface, we pursue analogy to some results known for moduli spaces of sheaves on a projective plane. We define an invariant height, introduced by Drezet in the projective plane case, for moduli spaces of sheaves with symmetric $c_{1}$ on a quadric surface and describe the structure of moduli spaces of height zero. Then we study rational maps of moduli spaces of positive height to moduli spaces of representation of quivers, effective cones of moduli spaces, and strange duality for height-zero moduli spaces.

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8

Schmitt, Alexander. "Stability Parameters for Quiver Sheaves." International Mathematics Research Notices 2020, no. 20 (October 2020): 6666–98. http://dx.doi.org/10.1093/imrn/rnz162.

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Abstract In this paper, we will begin the systematic study of the influence of the choice of a faithful representation on the notion of (semi)stability for decorated principal bundles. We will prove boundedness for slope semistable quiver sheaves.

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9

Argáez, A. S. "Examples of Stability of Tensor Products in Positive Characteristic." ISRN Algebra 2011 (September 19, 2011): 1–12. http://dx.doi.org/10.5402/2011/659672.

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Let X be projective smooth variety over an algebraically closed field k and let ℰ, ℱ be μ-semistable locally free sheaves on X. When the base field is ℂ, using transcendental methods, one can prove that the tensor product is always a μ-semistable sheaf. However, this theorem is no longer true over positive characteristic; for an analogous theorem one needs the hypothesis of strong μ-semistability; nevertheless, this hypothesis is not a necessary condition. The objective of this paper is to construct, without the strongly μ-semistability hypothesis, a family of locally free sheaves with μ-stable tensor product.

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10

Chen, Huachen. "O’Grady’s birational maps and strange duality via wall-hitting." International Journal of Mathematics 30, no. 09 (August 2019): 1950044. http://dx.doi.org/10.1142/s0129167x19500447.

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We prove that O’Grady’s birational maps [K. G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebr. Geom. 6(4) (1997) 599–644] between moduli of sheaves on an elliptic K3 surface can be interpreted as intermediate wall-crossing (wall-hitting) transformations at so-called totally semistable walls, studied by Bayer and Macrì [A. Bayer and E. Macrì, MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations, Inventiones Mathematicae 198(3) (2014) 505–590]. As a key ingredient, we describe the first totally semistable wall for ideal sheaves of [Formula: see text] points on the elliptic [Formula: see text]. As an application, we give new examples of strange duality isomorphisms, based on a result of Marian and Oprea [A. Marian and D. Oprea, Generic strange duality for K3 surfaces, with an appendix by Kota Yoshioka, Duke Math. J. 162(8) (2013) 1463–1501].

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11

Coskun, Izzet, and Jack Huizenga. "Existence of semistable sheaves on Hirzebruch surfaces." Advances in Mathematics 381 (April 2021): 107636. http://dx.doi.org/10.1016/j.aim.2021.107636.

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12

Langer, Adrian. "Addendum to “Semistable sheaves in positive characteristic”." Annals of Mathematics 160, no. 3 (November 1, 2004): 1211–13. http://dx.doi.org/10.4007/annals.2004.160.1211.

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13

Greb, Daniel, and Matei Toma. "Compact moduli spaces for slope-semistable sheaves." Algebraic Geometry 4, no. 1 (January 15, 2017): 40–78. http://dx.doi.org/10.14231/ag-2017-003.

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14

Abe, Takeshi. "Boundedness of semistable sheaves of rank four." Journal of Mathematics of Kyoto University 42, no. 2 (2002): 185–205. http://dx.doi.org/10.1215/kjm/1250283865.

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15

BHOSLE, USHA N. "BRILL–NOETHER THEORY ON NODAL CURVES." International Journal of Mathematics 18, no. 10 (November 2007): 1133–50. http://dx.doi.org/10.1142/s0129167x07004461.

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16

Mehta, V. B., and V. Trivedi. "On some Frobenius restriction theorems for semistable sheaves." Proceedings - Mathematical Sciences 119, no. 1 (February 2009): 109–18. http://dx.doi.org/10.1007/s12044-009-0011-6.

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17

Nakashima, Tohru. "Effective bounds for semistable sheaves on a threefold." Journal of Geometry and Physics 140 (June 2019): 271–79. http://dx.doi.org/10.1016/j.geomphys.2019.02.005.

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18

Langer, Adrian. "A note on restriction theorems for semistable sheaves." Mathematical Research Letters 17, no. 5 (2010): 823–31. http://dx.doi.org/10.4310/mrl.2010.v17.n5.a2.

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19

Yuan, Yao. "Motivic measures of moduli spaces of 1-dimensional sheaves on rational surfaces." Communications in Contemporary Mathematics 20, no. 03 (February 21, 2018): 1750019. http://dx.doi.org/10.1142/s0219199717500195.

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We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by computing their motivic measures.

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20

Bayer, Arend, Martí Lahoz, Emanuele Macrì, Howard Nuer, Alexander Perry, and Paolo Stellari. "Stability conditions in families." Publications mathématiques de l'IHÉS 133, no. 1 (May 17, 2021): 157–325. http://dx.doi.org/10.1007/s10240-021-00124-6.

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AbstractWe develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich–Polishchuk, Kuznetsov, Lieblich, and Piyaratne–Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers.Our main application is the generalization of Mukai’s theory for moduli spaces of semistable sheaves on K3 surfaces to moduli spaces of Bridgeland semistable objects in the Kuznetsov component associated to a cubic fourfold. This leads to the extension of theorems by Addington–Thomas and Huybrechts on the derived category of special cubic fourfolds, to a new proof of the integral Hodge conjecture, and to the construction of an infinite series of unirational locally complete families of polarized hyperkähler manifolds of K3 type.Other applications include the deformation-invariance of Donaldson–Thomas invariants counting Bridgeland stable objects on Calabi–Yau threefolds, and a method for constructing stability conditions on threefolds via degeneration.

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21

Ben-Zvi, David, and David Nadler. "Elliptic Springer theory." Compositio Mathematica 151, no. 8 (April 8, 2015): 1568–84. http://dx.doi.org/10.1112/s0010437x14008021.

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We introduce an elliptic version of the Grothendieck–Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the resolution of degree-zero, semistable $G$-bundles by degree-zero $B$-bundles over an elliptic curve $E$. From a representation theory perspective, they produce a full embedding of representations of the elliptic or double affine Weyl group into perverse sheaves with nilpotent characteristic variety on the moduli of $G$-bundles over $E$. The resulting objects are principal series examples of elliptic character sheaves, objects expected to play the role of character sheaves for loop groups.

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22

Hauzer, Marcin. "On moduli spaces of semistable sheaves on Enriques surfaces." Annales Polonici Mathematici 99, no. 3 (2010): 305–21. http://dx.doi.org/10.4064/ap99-3-7.

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23

Mozgovoy, Sergey, and Olivier Schiffmann. "Counting Higgs bundles and type quiver bundles." Compositio Mathematica 156, no. 4 (February 27, 2020): 744–69. http://dx.doi.org/10.1112/s0010437x20007010.

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We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus $g$ defined over a finite field, when the twisting line bundle degree is at least $2g-2$ (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson–Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver sheaves of type $A$ (finite or affine), obtaining in particular a Harder–Narasimhan-type formula counting semistable $U(p,q)$-Higgs bundles over a smooth projective curve defined over a finite field.

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24

Karpov, B. V. "SEMISTABLE SHEAVES ON A TWO-DIMENSIONAL QUADRIC, AND KRONECKER MODULES." Russian Academy of Sciences. Izvestiya Mathematics 40, no. 1 (February 28, 1993): 33–66. http://dx.doi.org/10.1070/im1993v040n01abeh001860.

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25

Maican, Mario. "The classification of semistable plane sheaves supported on sextic curves." Kyoto Journal of Mathematics 53, no. 4 (2013): 739–86. http://dx.doi.org/10.1215/21562261-2366086.

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26

Bhosle, Usha N. "Picard groups of the moduli spaces of semistable sheaves I." Proceedings Mathematical Sciences 114, no. 2 (May 2004): 107–22. http://dx.doi.org/10.1007/bf02829847.

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27

Toda, Yukinobu. "Moduli stacks of semistable sheaves and representations of Ext–quivers." Geometry & Topology 22, no. 5 (June 1, 2018): 3083–144. http://dx.doi.org/10.2140/gt.2018.22.3083.

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28

Karpov, B. V. "On the structure of rigid semistable sheaves on algebraic surfaces." Mathematical Notes 64, no. 5 (November 1998): 600–606. http://dx.doi.org/10.1007/bf02316284.

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29

Dimca, Alexandru, and Morihiko Saito. "Vanishing cycle sheaves of one-parameter smoothings and quasi-semistable degenerations." Journal of Algebraic Geometry 21, no. 2 (April 18, 2011): 247–71. http://dx.doi.org/10.1090/s1056-3911-2011-00572-9.

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30

Ivanov, Aleksei N., and Alexander S. Tikhomirov. "Semistable rank 2 sheaves with singularities of mixed dimension on P3." Journal of Geometry and Physics 129 (July 2018): 90–98. http://dx.doi.org/10.1016/j.geomphys.2018.02.018.

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31

Mozgovoy, Sergey. "Classification of semistable sheaves on a rational curve with one node." Journal of Algebra 323, no. 1 (January 2010): 14–26. http://dx.doi.org/10.1016/j.jalgebra.2009.09.007.

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32

Rössler, Damian. "Strongly semistable sheaves and the Mordell–Lang conjecture over function fields." Mathematische Zeitschrift 294, no. 3-4 (April 8, 2019): 1035–49. http://dx.doi.org/10.1007/s00209-019-02306-9.

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33

HU, YI. "RELATIVE GEOMETRIC INVARIANT THEORY AND UNIVERSAL MODULI SPACES." International Journal of Mathematics 07, no. 02 (April 1996): 151–81. http://dx.doi.org/10.1142/s0129167x96000098.

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We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the G-effective ample cone. We then apply this principle to construct and reconstruct various universal moduli spaces. In particular, we constructed the universal moduli space over [Formula: see text] of Simpson’s p-semistable coherent sheaves and a canonical rational morphism from the universal Hilbert scheme over [Formula: see text] to a compactified universal Picard.

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34

Lavrov, A. N. "A New Nonreduced Moduli Component of Rank-2 Semistable Sheaves on $ {𝕇}^{3} $." Siberian Mathematical Journal 63, no. 3 (May 2022): 509–19. http://dx.doi.org/10.1134/s0037446622030107.

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35

Yuan, Yao. "Moduli Spaces of Semistable Sheaves of Dimension $1$ on $\mathbb{P}^2$." Pure and Applied Mathematics Quarterly 10, no. 4 (2014): 723–66. http://dx.doi.org/10.4310/pamq.2014.v10.n4.a5.

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36

Pustetto, Andrea. "Mehta–Ramanathan for $$\varepsilon $$ ε and $$\textsf {k}$$ k -semistable decorated sheaves." Geometriae Dedicata 182, no. 1 (November 28, 2015): 133–62. http://dx.doi.org/10.1007/s10711-015-0132-2.

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37

Greb, Daniel, Stefan Kebekus, Thomas Peternell, and Behrouz Taji. "Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles." Compositio Mathematica 155, no. 2 (February 2019): 289–323. http://dx.doi.org/10.1112/s0010437x18007923.

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We generalise Simpson’s nonabelian Hodge correspondence to the context of projective varieties with Kawamata log terminal (klt) singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest form, this theorem asserts that given any klt variety$X$and any resolution of singularities, any vector bundle on the resolution that appears to come from$X$numerically, does indeed come from $X$. Furthermore, and of independent interest, a new restriction theorem for semistable Higgs sheaves defined on the smooth locus of a normal, projective variety is established.

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38

Greb, Daniel, and Matei Toma. "Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation." Journal de l’École polytechnique — Mathématiques 7 (January 15, 2020): 233–61. http://dx.doi.org/10.5802/jep.116.

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39

Maican, Mario. "A Duality Result for Moduli Spaces of Semistable Sheaves Supported on Projective Curves." Rendiconti del Seminario Matematico della Università di Padova 123 (2010): 55–68. http://dx.doi.org/10.4171/rsmup/123-3.

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40

Miesener, Michael. "On the Aut(A2)-action on G-semistable locally free sheaves on P2." Mathematische Nachrichten 286, no. 17-18 (July 16, 2013): 1833–49. http://dx.doi.org/10.1002/mana.201100158.

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41

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.

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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 $\mathbb{P}^{1}\times \mathbb{P}^{1}$.

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42

Abe, Takeshi. "Semistable sheaves with symmetric $$c_{1}$$ on Del Pezzo surfaces of degree 5 and 6." European Journal of Mathematics 7, no. 2 (January 8, 2021): 526–56. http://dx.doi.org/10.1007/s40879-020-00434-9.

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43

Migo-Roig, Rosa M. "Construction of Rank 2 Semistable Torsion Free Sheaves Which Are Not Limit of Vector Bundles." Manuscripta Mathematica 80, no. 1 (December 1993): 89–94. http://dx.doi.org/10.1007/bf03026539.

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44

Yamada, Kimiko. "Blowing-Ups Describing the Polarization Change of Moduli Schemes of Semistable Sheaves of General Rank." Communications in Algebra 38, no. 8 (August 13, 2010): 3094–110. http://dx.doi.org/10.1080/00927872.2010.481776.

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45

Zhao, Yigeng. "Duality for Relative Logarithmic de Rham-Witt Sheaves on Semistable Schemes over $\mathbb F_q[[t]]$." Documenta Mathematica 23 (2018): 1925–67. http://dx.doi.org/10.4171/dm/664.

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46

Tramel, Rebecca, and Bingyu Xia. "Bridgeland stability conditions on surfaces with curves of negative self-intersection." Advances in Geometry 22, no. 3 (July 1, 2022): 383–408. http://dx.doi.org/10.1515/advgeom-2022-0009.

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Abstract Let X be a smooth complex projective variety. In 2002, Bridgeland [6] defined a notion of stability for the objects in 𝔇 b (X), the bounded derived category of coherent sheaves on X, which generalised the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on X and the geometry of the variety. We construct new stability conditions for surfaces containing a curve C whose self-intersection is negative. We show that these stability conditions lie on a wall of the geometric chamber of Stab(X), the stability manifold of X.We then construct the moduli space Mσ (ℴ X ) of σ-semistable objects of class [ℴ X ] in K 0(X) after wall-crossing.

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47

Ivanov, A. N., and A. S. Tikhomirov. "The moduli component of the space of semistable rank-2 sheaves on ℙ3 with singularities of mixed dimension." Doklady Mathematics 96, no. 2 (September 2017): 506–9. http://dx.doi.org/10.1134/s1064562417050325.

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48

Ivanov, A. N. "A new series of moduli components of rank-2 semistable sheaves on $ {\mathbb{P}}^{3}$ with singularities of mixed dimension." Sbornik: Mathematics 211, no. 7 (July 2020): 967–86. http://dx.doi.org/10.1070/sm9312.

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49

Kytmanov, A. A., N. N. Osipov, and S. A. Tikhomirov. "On the Number of Irreducible Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space." Siberian Mathematical Journal 64, no. 1 (January 2023): 103–10. http://dx.doi.org/10.1134/s0037446623010123.

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50

Pedchenko, Dmitrii. "The Picard Group of the Moduli Space of Sheaves on a Quadric Surface." International Mathematics Research Notices, September 3, 2021. http://dx.doi.org/10.1093/imrn/rnab175.

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Abstract We study the Picard group of the moduli space of semistable sheaves on a smooth quadric surface. We polarize the surface by an ample divisor close to the anticanonical class. We focus especially on moduli spaces of sheaves of small discriminant, where we observe new and interesting behavior. Our method relies on constructing certain resolutions for semistable sheaves and applying techniques of geometric invariant theory to the resulting families of sheaves.

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