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We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space M of stable sheaves on a K3 surface X: 1.
Duality between D ( X ) D(X) and D ( X ^ ) D(\hat{X}) with its application to Picard sheaves
Shigeru Mukai · 1981
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Variétés Kähleriennes dont la première classe de Chern est nulle
Arnaud Beauville · 1983
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On K 3 K3 surfaces with large Picard number
D. R. Morrison · 1984
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Symplectic structure of the moduli space of sheaves on an abelian or K 3 K3 surface
Shigeru Mukai · 1984
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Pluricanonical systems on minimal algebraic varieties
Y. Kawamata · 1985
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On the moduli space of bundles on K 3 K3 surfaces. I
S. Mukai · 1987
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Fourier functor and its application to the moduli of bundles on an abelian variety
Shigeru Mukai · 1987
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Systèmes hamiltoniens complètement intégrables associés aux surfaces K 3 K3
A. Beauville · 1991
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Algebraic geometric interpretation of Donaldson’s polynomial invariants
Jun Li · 1993
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The cone of curves of a K 3 K3 surface
Sándor J. Kovács · 1994
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Variation of moduli spaces and Donaldson invariants under change of polarization
Geir Ellingsrud and Lothar Göttsche · 1995
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Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces
Robert Friedman and Zhenbo Qin · 1995
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Geometric invariant theory and flips
Michael Thaddeus · 1996
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Cohomology of compact hyper-Kähler manifolds and its applications
M. Verbitsky · 1996
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Mumford-Thaddeus principle on the moduli space of vector bundles on an algebraic surface
Kenji Matsuki and Richard Wentworth · 1997
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Equivalences of derived categories and K 3 K3 surfaces
D. O. Orlov · 1997
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Variation of geometric invariant theory quotients
Igor V. Dolgachev and Yi Hu · 1998
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Counting rational curves on K 3 K3 surfaces
Arnaud Beauville · 1999
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Compact hyper-Kähler manifolds: basic results
Daniel Huybrechts · 1999
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On fibre space structures of a projective irreducible symplectic manifold
Daisuke Matsushita · 1999
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Desingularized moduli spaces of sheaves on a K 3 K3
Kieran G. O’Grady · 1999
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Irreducibility of moduli spaces of vector bundles on K3 surfaces, 1999
Kōta Yoshioka · 1999
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Derived categories of twisted sheaves on Calabi-Yau manifolds
Andrei Căldăraru · 2000
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Calabi-Yau manifolds and related geometries
M. Gross, D. Huybrechts, and D. Joyce · 2001
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Rational curves on holomorphic symplectic fourfolds
B. Hassett and Y. Tschinkel · 2001
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Brill-Noether duality for moduli spaces of sheaves on K 3 K3 surfaces
Eyal Markman · 2001
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Addendum: “On fibre space structures of a projective irreducible symplectic manifold” [Topology 38
Daisuke Matsushita · 2001
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Deformation theory of singular symplectic n n -folds
Yoshinori Namikawa · 2001
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Braid group actions on derived categories of coherent sheaves
Paul Seidel and Richard Thomas · 2001
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Moduli spaces of stable sheaves on abelian surfaces
Kōta Yoshioka · 2001
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Nonfine moduli spaces of sheaves on K 3 K3 surfaces
Andrei Căldăraru · 2002
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The Kähler cone of a compact hyperkähler manifold
Daniel Huybrechts · 2003
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Abelian fibred holomorphic symplectic manifolds
Justin Sawon · 2003
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Contractions of symplectic varieties
Jan Wierzba · 2003
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Divisorial Zariski decompositions on compact complex manifolds
Sébastien Boucksom · 2004
Cited alongside, same era.
Autoequivalences of derived category of a K 3 K3 surface and monodromy transformations
Shinobu Hosono, Bong H. Lian, Keiji Oguiso, and Shing-Tung Yau · 2004
Cited alongside, same era.
Equivalences of twisted K 3 K3 surfaces
Daniel Huybrechts and Paolo Stellari · 2005
Cited alongside, same era.
Dualité étrange, sur les surfaces, 2005
Joseph Le Potier · 2005
Cited alongside, same era.
Groups of autoequivalences of derived categories of smooth projective varieties, 2005
David Ploog · 2005
Cited alongside, same era.
Sheaves of t t -structures and valuative criteria for stable complexes
Dan Abramovich and Alexander Polishchuk · 2006
Cited alongside, same era.
Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities, 2011
Arend Bayer, Emanuele Macrì, and Yukinobu Toda · 2011
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The birational geometry of moduli space of sheaves on the projective plane, 2013
Aaron Bertram, Cristian Martinez, and Jie Wang · 2011
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Osamu Fujino · 2011
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Lagrangian fibrations on hyperkähler fourfolds, 2011
Daniel Greb, Christian Lehn, and Sönke Rollenske · 2011
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Lagrangian fibrations on hyperkähler manifolds - On a question of Beauville, 2011
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Proof of Căldăraru’s conjecture. Appendix to: “Moduli spaces of twisted sheaves on a projective variety” by K. Yoshioka
Daniel Huybrechts and Paolo Stellari · 2006
Cited alongside, same era.
Singular symplectic moduli spaces
D. Kaledin, M. Lehn, and Ch. Sorger · 2006
Cited alongside, same era.
Rational Lagrangian fibrations on punctual Hilbert schemes of K 3 K3 surfaces
Dimitri Markushevich · 2006
Cited alongside, same era.
Moduli spaces of twisted sheaves on a projective variety
Kōta Yoshioka · 2006
Cited alongside, same era.
Stability conditions on triangulated categories
Tom Bridgeland · 2007
Cited alongside, same era.
Moduli of twisted sheaves
Max Lieblich · 2007
Cited alongside, same era.
Daniel Greb, Christian Lehn, and Sönke Rollenske · 2011
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A global Torelli theorem for hyperkähler manifolds (after Verbitsky), 2011
Daniel Huybrechts · 2011
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Jason Lo and Zhenbo Qin · 2011
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A survey of Torelli and monodromy results for holomorphic-symplectic varieties
Eyal Markman · 2011
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Fourier-mukai transforms and the wall-crossing behavior for Bridgeland’s stability conditions, 2011
Hiroki Minamide, Shintarou Yanagida, and Kōta Yoshioka · 2011
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Some moduli spaces of Bridgeland’s stability conditions, 2011
Hiroki Minamide, Shintarou Yanagida, and Kōta Yoshioka · 2011
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A remark on a question of Beauville about lagrangian fibrations
Ekaterina Amerik · 2012
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Projectivity and birational geometry of Bridgeland moduli spaces, 2012
Arend Bayer and Emanuele Macrì · 2012
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Ciro Ciliberto and Andreas Leopold Knutsen · 2012
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Cusps of the Kähler moduli space and stability conditions on K3 surfaces
Heinrich Hartmann · 2012
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Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces
David Harvey, Brendan Hassett, and Yuri Tschinkel · 2012
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Jack Huizenga · 2012
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On some moduli of complexes on K 3 {K}3 surfaces, 2012
Jason Lo · 2012
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Computing the walls associated to Bridgeland stability conditions on projective surfaces, 2012
Antony Maciocia · 2012
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On almost holomorphic Lagrangian fibrations, 2012
Daisuke Matsushita · 2012
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Hilbert schemes of K3 surfaces are dense in moduli, 2012
Eyal Markman and Sukhendu Mehrotra · 2012
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Kōta Yoshioka · 2012
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Bridgeland’s stabilities on abelian surfaces, 2012
Shintarou Yanagida and Kōta Yoshioka · 2012
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Bridgeland-stable moduli spaces for K K -trivial surfaces
Daniele Arcara and Aaron Bertram · 2013
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Daniele Arcara, Aaron Bertram, Izzet Coskun, and Jack Huizenga · 2013
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The birational geometry of the Hilbert scheme of points on surfaces
Aaron Bertram and Izzet Coskun · 2013
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Mori cones of holomorphic symplectic varieties of K3 type, 2013
Arend Bayer, Brendan Hassett, and Yuri Tschinkel · 2013
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Alternate compactifications of moduli spaces of curves
Maksym Fedorchuk and David Ishii Smyth · 2013
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Webs of Lagrangian tori in projective symplectic manifolds
Jun-Muk Hwang and Richard M. Weiss · 2013
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Lagrangian fibrations of holomorphic-symplectic varieties of K 3 [ n ] {K3}^{[n]} -type, 2013
Eyal Markman · 2013
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Prime exceptional divisors on holomorphic symplectic varieties and monodromy-reflections
Eyal Markman · 2013
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On isotropic divisors on irreducible symplectic manifolds, 2013
Daisuke Matsushita · 2013
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Rank one Bridgeland stable moduli spaces on a principally polarized abelian surface
Antony Maciocia and Ciaran Meachan · 2013
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A note on the Kähler and Mori cones of manifolds of K 3 [ n ] {K3}^{[n]} type, 2013
Giovanni Mongardi · 2013
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