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Опубліковано: 14 березня 2023

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Статті в журналах з теми "Moduli spaces of sheaves on surfaces"

1

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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2

Sawon, Justin. "Moduli spaces of sheaves on K3 surfaces." Journal of Geometry and Physics 109 (November 2016): 68–82. http://dx.doi.org/10.1016/j.geomphys.2016.02.017.

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3

Yoshioka, Kōta. "Moduli spaces of stable sheaves on Enriques surfaces." Kyoto Journal of Mathematics 58, no. 4 (December 2018): 865–914. http://dx.doi.org/10.1215/21562261-2017-0037.

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4

Yoshioka, Kōta. "Moduli spaces of stable sheaves on abelian surfaces." Mathematische Annalen 321, no. 4 (December 1, 2001): 817–84. http://dx.doi.org/10.1007/s002080100255.

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5

Camere, Chiara, Grzegorz Kapustka, Michał Kapustka, and Giovanni Mongardi. "Verra Four-Folds, Twisted Sheaves, and the Last Involution." International Mathematics Research Notices 2019, no. 21 (February 1, 2018): 6661–710. http://dx.doi.org/10.1093/imrn/rnx327.

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Abstract We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3[2]-type admitting non-symplectic involutions with invariant lattices U(2) ⊕ D4(−1) or U(2) ⊕ E8(−2). This complements the results obtained in [43], [13], and the results from [29] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using the Hilbert scheme of (1, 1) conics on Verra four-folds. As a byproduct we find that IHS four-folds of K3[2]-type with Picard lattice U(2) ⊕ E8(−2) naturally contain non-nodal Enriques surfaces.
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6

Onishi, Nobuaki, and Kōta Yoshioka. "Singularities on the 2-Dimensional Moduli Spaces of Stable Sheaves on K3 Surfaces." International Journal of Mathematics 14, no. 08 (October 2003): 837–64. http://dx.doi.org/10.1142/s0129167x03002022.

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We consider the singuralities of 2-dimensional moduli spaces of semi-stable sheaves on k3 surfaces. We show that the moduli space is normal, in particular the siguralities are rational double points. We also describe the exceptional locus on the resolution in terms of exceptional sheaves.
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7

Yoshioka, Kōta. "Some notes on the moduli of stable sheaves on elliptic surfaces." Nagoya Mathematical Journal 154 (1999): 73–102. http://dx.doi.org/10.1017/s0027763000025319.

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AbstractIn this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman’s results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on ℙ2 are rational. We also compute the Picard groups of those on Abelian surfaces.
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8

HALIC, MIHAI, and ROSHAN TAJAROD. "A cohomological splitting criterion for locally free sheaves on arithmetically Cohen–Macaulay surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 155, no. 3 (July 3, 2013): 517–27. http://dx.doi.org/10.1017/s0305004113000406.

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AbstractIn this paper we obtain a cohomological splitting criterion for locally free sheaves on arithmetically Cohen–Macaulay surfaces with cyclic Picard group, which is similar to Horrocks' splitting criterion for locally free sheaves on projective spaces. We also recover a duality property which identifies a general K3 surface with a certain moduli space of stable sheaves on it, and obtain examples of stable, arithmetically Cohen–Macaulay, locally free sheaves of rank two on general surfaces of degree at least five in ${\mathbb P}^3$.
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9

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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10

Manschot, Jan, and Sergey Mozgovoy. "Intersection cohomology of moduli spaces of sheaves on surfaces." Selecta Mathematica 24, no. 5 (August 14, 2018): 3889–926. http://dx.doi.org/10.1007/s00029-018-0431-1.

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Дисертації з теми "Moduli spaces of sheaves on surfaces"

1

Bridgeland, Tom. "Fourier-Mukai transforms for surfaces and moduli spaces of stable sheaves." Thesis, University of Edinburgh, 2002. http://hdl.handle.net/1842/12070.

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In this thesis we study Fourier-Mukai transforms for complex projective surfaces. Extending work of A.I. Bondal and D.O. Orlov, we prove a theorem giving necessary and sufficient conditions for a functor between the derived categories of sheaves on two smooth projective varieties to be an equivalence of categories, and use it to construct examples of Fourier-Mukai transforms for surfaces. In particular we construct new transforms for elliptic surfaces and quotient surfaces. This enables us to identify all pairs of complex projective surfaces having equivalent derived categories of sheaves. We also derive some general properties of Fourier-Mukai transforms, and gives examples of their use. The main applications are to the study of moduli spaces of stable sheaves. In particular we identify many such moduli spaces on elliptic surfaces, generalising results of R. Friedman.
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2

Scalise, Jacopo Vittorio. "Frames symplectic sheaves on surfaces and their ADHM data." Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/4896.

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This dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP−bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C.
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3

Hoskins, Victoria Amy. "Moduli spaces of complexes of sheaves." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:aedd2719-2a38-41f9-9825-aa8f43fb872c.

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This thesis is on moduli spaces of complexes of sheaves and diagrams of such moduli spaces. The objects in these diagrams are constructed as geometric invariant theory quotients and the points in these quotients correspond to certain equivalence classes of complexes. The morphisms in these diagrams are constructed by taking direct sums with acyclic complexes. We then study the colimit of such a diagram and in particular are interested in studying the images of quasi-isomorphic complexes in the colimit. As part of this thesis we construct categorical quotients of a group action on unstable strata appearing in a stratification associated to a complex projective scheme with a reductive group action linearised by an ample line bundle. We study this stratification for a closed subscheme of a quot scheme parametrising quotient sheaves over a complex projective scheme and relate the Harder-Narasimhan types of unstable sheaves with the unstable strata in the associated stratification. We also study the stratification of a parameter space for complexes with respect to a linearisation determined by certain stability parameters and show that a similar result holds in this case. The objects in these diagrams are indexed by different Harder-Narasimhan types for complexes and are quotients of parameter schemes for complexes of this fixed Harder-Narasimhan type. This quotient is given by a choice of linearisation of the action and so the diagrams depend on these choices. We conjecture that these choices can be made so that for any quasi-isomorphism between complexes representing points in this diagram both complexes are identified in the colimit of this diagram.
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4

Kool, Martijn. "Moduli spaces of sheaves on toric varieties." Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526468.

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5

Abdellaoui, Gharchia. "Topology of moduli spaces of framed sheaves." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4806.

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6

Nironi, Fabio. "Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks." Doctoral thesis, SISSA, 2008. http://hdl.handle.net/20.500.11767/4165.

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7

Sala, Francesco. "Some topics in the geometry of framed sheaves and their moduli spaces." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4129.

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This dissertation is primarily concerned with the study of framed sheaves on nonsingular projective varieties and the geometrical properties of the moduli spaces of these objects. In particular, we deal with a generalization to the framed case of known results for (semi)stable torsion free sheaves, such as (relative) Harder-Narasimhan filtration, Mehta-Ramanathan restriction theorems, Uhlenbeck-Donaldson compactification, Atiyah class and Kodaira-Spencer map. The main motivations for the study of these moduli spaces come from physics, in particular, gauge theory, as we shall explain in the following.
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Sala, Francesco. "Some topics in the geometry of framed sheaves and their moduli spaces." Thesis, Lille 1, 2011. http://www.theses.fr/2011LIL10076/document.

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La thèse est consacrée à l'étude des faisceaux encadrés sur des variétés non-singulières projectives et des propriétés géométriques de leurs espaces de modules. En particulier, on donne une généralisation au cas encadré des résultats connus pour les faisceaux (semi)stables sans torsion non-encadrés, comme l'existence de la filtration de Harder-Narasimhan (relative), théorèmes de restriction de Mehta-Ramanathan, compactification de Donaldson-Uhlenbeck, la définition de la classe d'Atiyah relative et la description de l'application de Kodaira-Spencer via la classe d'Atiyah relative, l'existence d'une structure symplectique holomorphe, dans certains cas, sur les espaces de modules de faisceaux encadrés
The thesis is concerned with the study of framed sheaves on nonsingular projective varieties and the geometrical properties of their moduli spaces. In particular, it deals with a generalization to the framed case of known results for (semi)stable torsion free nonframed sheaves, such as the existence of the (relative) Harder-Narasimhan filtration, Mehta-Ramanathan restriction theorems, Uhlenbeck-Donaldson compactification, the definition of the relative Atiyah class and the description of the Kodaira-Spencer map in terms of the relative Atiyah class, the existence of a symplectic structure, in certain cases, on the moduli spaces of framed sheaves
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9

Schlüeter, Dirk Christopher. "Universal moduli of parabolic sheaves on stable marked curves." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:b0260f8e-6654-4bec-b670-5e925fd403dd.

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The topic of this thesis is the moduli theory of (parabolic) sheaves on stable curves. Using geometric invariant theory (GIT), universal moduli spaces of semistable parabolic sheaves on stable marked curves are constructed: `universal' indicates that these are moduli spaces of pairs where the underlying marked curve may vary as well as the parabolic sheaf (as in the Pandharipande moduli space for pairs of stable curves and torsion-free sheaves without augmentations). As an intermediate step in this construction, we construct moduli spaces of semistable parabolic sheaves on flat families of arbitrary projective schemes (of any dimension or singularity type): this is the technical core of this thesis. These moduli spaces are projective, since they are constructed as GIT quotients of projective parameter spaces. The stability condition for parabolic sheaves depends on a choice of polarisation and is derived from the Hilbert-Mumford criterion. It is not quite the same as traditional stability with respect to parabolic Hilbert polynomials, but it is closely related to it, and the resulting moduli spaces are always compactifications of moduli of slope-stable parabolic sheaves. The construction works over algebraically closed fields of arbitrary characteristic.
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10

Marque, Nicolas. "Moduli spaces of Willmore immersions." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7127.

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Dans ce travail doctoral, nous commençons par présenter une synthèse du formalisme des immersions faibles de Willmore. A cet effet, nous introduisons les lois de conservation et les exploitons pour retrouver les résultats d'epsilon régularité, ainsi qu'un résultat de régularité faible inédit. Nous présentons ensuite une étude de l'application de Gauss conforme et de ses liens avec la notion de surface de Willmore. Nous en déduisons une loi d'échange de résidus ainsi que d'une caractérisation originale des surfaces étant transformations de surfaces à courbure moyenne constante. Nous appliquons ensuite ces outils aux suites d'immersions de Willmore. Nous montrons tout d'abord qu'elles ne sont pas compactes avec un premier exemple de concentration pour les surfaces de Willmore. Cependant, en se basant sur un résultat d'epsilon régularité demandant un contrôle sur la courbure moyenne, nous montrons une compacité sous un certain plafond d'énergie
In this doctoral work we start by exposing a synthesis of the weak Willmore immersions formalism. To that end, we introduce conservation laws and exploit them to recover the epsilon-regularity theorems, as well as an innovative weak regularity result. We then present a study of the conformal Gauss map and its links with the Willmore surface notion. From this, we deduce an exchange law for residues as well as an original caracterization of surfaces that are conformal transforms of constant mean curvature surfaces. We then apply these tools to sequences of Willmore immersions. We first show that they are not compact wth a first instance of concentration for Willmore surfaces. However, relying upon an epsilon-regularity result based on a small control on the mean curvature, we show compactness below a given threshold
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Книги з теми "Moduli spaces of sheaves on surfaces"

1

Huybrechts, Daniel. The geometry of moduli spaces of sheaves. Braunschweig: Vieweg, 1997.

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2

Manfred, Lehn, ed. The geometry of moduli spaces of sheaves. 2nd ed. Cambridge, UK: Cambridge University Press, 2010.

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3

Huybrechts, Daniel. The geometry of moduli spaces of sheaves. 2nd ed. Cambridge, UK: Cambridge University Press, 2010.

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4

Huybrechts, Daniel, and Manfred Lehn. The Geometry of Moduli Spaces of Sheaves. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0.

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5

Hain, Richard M., Eduard Looijenga, and Benson Farb. Moduli spaces of Riemann surfaces. Providence, Rhode Island: American Mathematical Society, 2013.

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6

1776-1853, Hoene-Wroński Józef Maria, and Pragacz Piotr, eds. Algebraic cycles, sheaves, shtukas, and moduli. Basel: Birkhäuser, 2008.

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7

Göttsche, Lothar. Moduli spaces in algebraic geometry: 2000. Trieste, Italy: ICTP--The Abdus Salam International Centre for Theoretical Physics, 2000.

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8

Casella, Alex. Moduli spaces of real projective structures on surfaces. Tokyo: The Mathematical Society of Japan, 2020.

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9

Bödigheimer, Carl-Friedrich, and Richard M. Hain, eds. Mapping Class Groups and Moduli Spaces of Riemann Surfaces. Providence, Rhode Island: American Mathematical Society, 1993. http://dx.doi.org/10.1090/conm/150.

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10

Izquierdo, Milagros, S. Broughton, Antonio Costa, and Rubí Rodríguez, eds. Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces. Providence, Rhode Island: American Mathematical Society, 2014. http://dx.doi.org/10.1090/conm/629.

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Частини книг з теми "Moduli spaces of sheaves on surfaces"

1

Huybrechts, Daniel, and Manfred Lehn. "Moduli Spaces on K3 Surfaces." In The Geometry of Moduli Spaces of Sheaves, 141–59. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0_6.

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2

Coskun, Izzet, and Jack Huizenga. "The Moduli Spaces of Sheaves on Surfaces, Pathologies and Brill-Noether Problems." In Geometry of Moduli, 75–105. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94881-2_4.

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3

Neguţ, Andrei. "Moduli Spaces of Sheaves on Surfaces: Hecke Correspondences and Representation Theory." In Lecture Notes in Mathematics, 53–81. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26856-5_2.

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4

Huybrechts, Daniel, and Manfred Lehn. "Moduli Spaces." In The Geometry of Moduli Spaces of Sheaves, 79–118. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0_4.

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Huybrechts, Daniel, and Manfred Lehn. "Families of Sheaves." In The Geometry of Moduli Spaces of Sheaves, 32–56. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0_2.

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6

A’Campo, Norbert. "Moduli Spaces and Teichmüller Spaces." In Topological, Differential and Conformal Geometry of Surfaces, 219–25. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89032-2_14.

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Huybrechts, Daniel, and Manfred Lehn. "Restriction of Sheaves to Curves." In The Geometry of Moduli Spaces of Sheaves, 160–77. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0_7.

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8

Howard, Benjamin, and Tonghai Yang. "Moduli Spaces of Abelian Surfaces." In Intersections of Hirzebruch–Zagier Divisors and CM Cycles, 25–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23979-3_3.

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9

Huybrechts, Daniel, and Manfred Lehn. "Line Bundles on the Moduli Space." In The Geometry of Moduli Spaces of Sheaves, 178–98. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0_8.

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Flenner, Hubert, and Martin Lübke. "Analytic Moduli Spaces of Simple (Co)Framed Sheaves." In Complex Geometry, 99–109. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56202-0_7.

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