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Journal articles on the topic 'Moduli spaces of sheaves on surfaces'

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Published: 14 March 2023

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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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11

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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12

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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13

Toda, Yukinobu. "Stability conditions and birational geometry of projective surfaces." Compositio Mathematica 150, no. 10 (July 17, 2014): 1755–88. http://dx.doi.org/10.1112/s0010437x14007337.

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AbstractWe show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

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14

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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15

Sala, Francesco. "Symplectic structures on moduli spaces of framed sheaves on surfaces." Central European Journal of Mathematics 10, no. 4 (May 2, 2012): 1455–71. http://dx.doi.org/10.2478/s11533-012-0063-1.

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16

Langer, Adrian. "Moduli spaces and Castelnuovo-Mumford regularity of sheaves on surfaces." American Journal of Mathematics 128, no. 2 (2006): 373–417. http://dx.doi.org/10.1353/ajm.2006.0014.

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17

Zhang, Ziyu. "Moduli spaces of sheaves on K3 surfaces and symplectic stacks." Communications in Analysis and Geometry 25, no. 5 (2017): 1063–106. http://dx.doi.org/10.4310/cag.2017.v25.n5.a6.

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18

Zowislok, Markus. "On moduli spaces of sheaves on K3 or abelian surfaces." Mathematische Zeitschrift 272, no. 3-4 (February 4, 2012): 1195–217. http://dx.doi.org/10.1007/s00209-012-0983-2.

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19

Bottacin, Francesco. "Poisson structures on moduli spaces of sheaves over Poisson surfaces." Inventiones Mathematicae 121, no. 1 (December 1995): 421–36. http://dx.doi.org/10.1007/bf01884307.

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20

Toma, Matei. "Compact moduli spaces of stable sheaves over non-algebraic surfaces." Documenta Mathematica 6 (2001): 9–27. http://dx.doi.org/10.4171/dm/94.

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21

NEVINS, THOMAS A. "MODULI SPACES OF FRAMED SHEAVES ON CERTAIN RULED SURFACES OVER ELLIPTIC CURVES." International Journal of Mathematics 13, no. 10 (December 2002): 1117–51. http://dx.doi.org/10.1142/s0129167x02001599.

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Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve C; we study the moduli problem of parametrizing certain pairs consisting of a sheaf ℰ on S and a map of ℰ to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the group C*, and we determine its fixed-point set, which leads to explicit formulas for the rational homology of the moduli space.

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22

Choi, Jinwon, Michel van Garrel, Sheldon Katz, and Nobuyoshi Takahashi. "Local BPS Invariants: Enumerative Aspects and Wall-Crossing." International Mathematics Research Notices 2020, no. 17 (August 2, 2018): 5450–75. http://dx.doi.org/10.1093/imrn/rny171.

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Abstract We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincaré polynomials of the moduli spaces for the curve classes $\beta $ having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of $((-K_S).\beta -1)$-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].

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23

Drézet, Jean-Marc. "Reachable sheaves on ribbons and deformations of moduli spaces of sheaves." International Journal of Mathematics 28, no. 12 (November 2017): 1750086. http://dx.doi.org/10.1142/s0129167x17500860.

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A primitive multiple curve is a Cohen–Macaulay irreducible projective curve [Formula: see text] that can be locally embedded in a smooth surface, and such that [Formula: see text] is smooth. In this case, [Formula: see text] is a line bundle on [Formula: see text]. If [Formula: see text] is of multiplicity 2, i.e. if [Formula: see text], [Formula: see text] is called a ribbon. If [Formula: see text] is a ribbon and [Formula: see text], then [Formula: see text] can be deformed to smooth curves, but in general a coherent sheaf on [Formula: see text] cannot be deformed in coherent sheaves on the smooth curves. It has been proved in [Reducible deformations and smoothing of primitive multiple curves, Manuscripta Math. 148 (2015) 447–469] that a ribbon with associated line bundle [Formula: see text] such that [Formula: see text] can be deformed to reduced curves having two irreducible components if [Formula: see text] can be written as [Formula: see text] where [Formula: see text] are distinct points of [Formula: see text]. In this case we prove that quasi-locally free sheaves on [Formula: see text] can be deformed to torsion-free sheaves on the reducible curves with two components. This has some consequences on the structure and deformations of the moduli spaces of semi-stable sheaves on [Formula: see text].

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24

Ballico, Edoardo, and Sukmoon Huh. "Stable Sheaves on a Smooth Quadric Surface with Linear Hilbert Bipolynomials." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/346126.

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We investigate the moduli spaces of stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial in some special cases and describe their geometry in terms of the locally free resolution of the sheaves.

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25

Addington, Nicolas, Will Donovan, and Ciaran Meachan. "Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences." Journal of the London Mathematical Society 93, no. 3 (May 13, 2016): 846–65. http://dx.doi.org/10.1112/jlms/jdw022.

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26

Markman, Eyal. "On the monodromy of moduli spaces of sheaves on K3 surfaces." Journal of Algebraic Geometry 17, no. 1 (January 1, 2008): 29–99. http://dx.doi.org/10.1090/s1056-3911-07-00457-2.

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27

Göttsche, Lothar. "Rationality of moduli spaces of torsion free sheaves over rational surfaces." Manuscripta Mathematica 89, no. 1 (December 1996): 193–201. http://dx.doi.org/10.1007/bf02567513.

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28

Zhang, Ziyu. "A note on singular moduli spaces of sheaves on K3 surfaces." Geometriae Dedicata 173, no. 1 (January 3, 2014): 347–63. http://dx.doi.org/10.1007/s10711-013-9946-y.

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29

Maican, Mario. "Moduli of stable sheaves supported on curves of genus three contained in a quadric surface." Advances in Geometry 20, no. 4 (October 27, 2020): 507–22. http://dx.doi.org/10.1515/advgeom-2019-0025.

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AbstractWe study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.

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30

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.

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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.

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31

Kool, Martijn. "Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces." Geometriae Dedicata 176, no. 1 (February 19, 2014): 241–69. http://dx.doi.org/10.1007/s10711-014-9966-2.

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32

Bruzzo, Ugo, Rubik Poghossian, and Alessandro Tanzini. "Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces." Communications in Mathematical Physics 304, no. 2 (April 8, 2011): 395–409. http://dx.doi.org/10.1007/s00220-011-1231-z.

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33

Perego, Arvid, and Antonio Rapagnetta. "Factoriality Properties of Moduli Spaces of Sheaves on Abelian and K3 Surfaces." International Mathematics Research Notices 2014, no. 3 (October 29, 2012): 643–80. http://dx.doi.org/10.1093/imrn/rns233.

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34

Göttsche, Lothar. "Theta Functions and Hodge Numbers of Moduli Spaces of Sheaves on Rational Surfaces." Communications in Mathematical Physics 206, no. 1 (September 1, 1999): 105–36. http://dx.doi.org/10.1007/s002200050699.

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35

Arbarello, E., and G. Saccà. "Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima quiver varieties." Advances in Mathematics 329 (April 2018): 649–703. http://dx.doi.org/10.1016/j.aim.2018.02.003.

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36

Markman, Eyal. "Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces." Advances in Mathematics 208, no. 2 (January 2007): 622–46. http://dx.doi.org/10.1016/j.aim.2006.03.006.

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37

Garcia-Fernandez, Mario. "T-dual solutions of the Hull–Strominger system on non-Kähler threefolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 766 (September 1, 2020): 137–50. http://dx.doi.org/10.1515/crelle-2019-0013.

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AbstractWe construct new examples of solutions of the Hull–Strominger system on non-Kähler torus bundles over K3 surfaces, with the property that the connection {\nabla} on the tangent bundle is Hermite–Yang–Mills. With this ansatz for the connection {\nabla}, we show that the existence of solutions reduces to known results about moduli spaces of slope-stable sheaves on a K3 surface, combined with elementary analytical methods. We apply our construction to find the first examples of T-dual solutions of the Hull–Strominger system on compact non-Kähler manifolds with different topology.

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38

Lieblich, Max. "Twisted sheaves and the period-index problem." Compositio Mathematica 144, no. 1 (January 2008): 1–31. http://dx.doi.org/10.1112/s0010437x07003144.

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AbstractWe use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber’s theorem that they coincide for a separated union of two affine schemes), (2) give a new proof of de Jong’s period-index theorem for surfaces over algebraically closed fields, and (3) prove an analogous result for surfaces over finite fields. We also include a reduction of all period-index problems for Brauer groups of function fields over algebraically closed fields to characteristic zero, which (among other things) extends de Jong’s result to include classes of period divisible by the characteristic of the base field. Finally, we use the theory developed here to give counterexamples to a standard type of local-to-global conjecture for geometrically rational varieties over the function field of the projective plane.

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39

Qin, Zhenbo. "Birational properties of moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces." Manuscripta Mathematica 72, no. 1 (December 1991): 163–80. http://dx.doi.org/10.1007/bf02568273.

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40

Göttsche, Lothar. "Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces." Mathematische Zeitschrift 223, no. 1 (September 1996): 247–60. http://dx.doi.org/10.1007/bf02621597.

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41

Yuan, Yao. "Determinant line bundles on moduli spaces of pure sheaves on rational surfaces and strange duality." Asian Journal of Mathematics 16, no. 3 (2012): 451–78. http://dx.doi.org/10.4310/ajm.2012.v16.n3.a6.

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42

Göttsche, Lothar. "Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces." Mathematische Zeitschrift 223, no. 2 (October 1996): 247–60. http://dx.doi.org/10.1007/pl00004557.

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43

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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44

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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45

Yuan, Yao. "Estimates of sections of determinant line bundles on Moduli spaces of pure sheaves on algebraic surfaces." Manuscripta Mathematica 137, no. 1-2 (April 17, 2011): 57–79. http://dx.doi.org/10.1007/s00229-011-0457-6.

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46

Nuer, Howard, and Kōta Yoshioka. "MMP via wall-crossing for moduli spaces of stable sheaves on an Enriques surface." Advances in Mathematics 372 (October 2020): 107283. http://dx.doi.org/10.1016/j.aim.2020.107283.

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47

Choy, Jae-Yoo, and Young-Hoon Kiem. "NONEXISTENCE OF A CREPANT RESOLUTION OF SOME MODULI SPACES OF SHEAVES ON A K3 SURFACE." Journal of the Korean Mathematical Society 44, no. 1 (January 31, 2007): 35–54. http://dx.doi.org/10.4134/jkms.2007.44.1.035.

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48

Biswas, Indranil, and Tomás L. Gómez. "Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface." Geometriae Dedicata 207, no. 1 (October 26, 2019): 157–65. http://dx.doi.org/10.1007/s10711-019-00490-w.

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49

Kiem, Young-Hoon. "On the existence of a symplectic desingularization of some moduli spaces of sheaves on a K3 surface." Compositio Mathematica 141, no. 04 (June 21, 2005): 902–6. http://dx.doi.org/10.1112/s0010437x05001272.

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50

Choy, Jaeyoo, and Young-Hoon Kiem. "On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface." Mathematische Zeitschrift 252, no. 3 (November 19, 2005): 557–75. http://dx.doi.org/10.1007/s00209-005-0866-x.

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