Derived and abelian equivalence of K3 surfaces

DOI10.1090/S1056-3911-07-00481-XzbMath1157.14021arXivmath/0604150OpenAlexW1804348296MaRDI QIDQ5460233

Daniel Huybrechts

Publication date: 5 May 2008

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604150

zbMATH Keywords

stability conditions\(K3\) surfacesderived equivalenceabelian equivalenceFourier-Mukai transformscomplexified polarization

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28)

Related Items

Critical \(k\)-very ampleness for abelian surfaces ⋮ Perverse coherent sheaves and Fourier-Mukai transforms on surfaces. I. ⋮ Motives of derived equivalent \(K3\) surfaces ⋮ MODULI SPACES OF STABLE BUNDLES ON K3 FIBERED CALABI–YAU THREEFOLDS ⋮ Stability of Gieseker stable sheaves on \(K3\) surfaces in the sense of Bridgeland and some applications ⋮ Fourier-Mukai duality for \(K3\) surfaces via Bridgeland stability condition ⋮ Co-t-structures, cotilting and cotorsion pairs ⋮ Cusps of the Kähler moduli space and stability conditions on \(K3\) surfaces ⋮ Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants ⋮ MMP for moduli of sheaves on \(K3\)s via wall-crossing: nef and movable cones, Lagrangian fibrations ⋮ Self-orthogonal \(\tau\)-tilting modules and tilting modules ⋮ The wall-crossing behavior for Bridgeland's stability conditions on abelian and \(K3\) surfaces ⋮ Stability and the Fourier–Mukai transform II ⋮ Derived equivalences via HRS-tilting ⋮ Fourier-Mukai transforms of slope stable torsion-free sheaves on a product elliptic threefold ⋮ Perverse coherent sheaves and Fourier-Mukai transforms on surfaces. II.

Cites Work

• Equivalences of derived categories and \(K3\) surfaces
• The irreducible components of moduli spaces of vector bundles on surfaces
• Stability and the Fourier-Mukai transform. I
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• Classification of holomorphic vector bundles on noncommutative two-tori
• Stability conditions on \(K3\) surfaces
• Stability conditions on triangulated categories
• Equivalences of twisted K3 surfaces
• A Fourier-Mukai Transform for Stable Bundles on K3 Surfaces
• GENERALIZED CALABI–YAU STRUCTURES, K3 SURFACES, AND B-FIELDS
• Tilting in abelian categories and quasitilted algebras
• Des catégories abéliennes
• Moduli spaces of stable sheaves on abelian surfaces.
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