Fourier--Mukai transforms for Gorenstein schemes

DOI10.1016/j.aim.2006.09.006zbMath1118.14022arXivmath/0506593OpenAlexW2150706552MaRDI QIDQ877734

Ana Cristina López Martín, Fernando Sancho de Salas, Daniel Hernandez Ruiperez

Publication date: 3 May 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506593

zbMATH Keywords

elliptic fibrationderived categoryspanning classD-equivalencefully faithful integral transformMukai pairstrongly simple

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items

Fully faithfulness criteria for quasi-projective schemes, Fully faithful Fourier-Mukai functors and generic vanishing, Reconstructing schemes from the derived category, A note on semiorthogonal indecomposability of some Cohen-Macaulay varieties, On equivalences of derived and singular categories, Twisting derived equivalences, Derived equivalences and Kodaira fibers, Adjoints to a Fourier-Mukai functor, Flops and spherical functors, Semiorthogonal decomposition via categorical action, Reconstruction of projective curves from the derived category, Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds, Relative perfect complexes, Fourier-Mukai partners of singular genus one curves, On a relative Fourier-Mukai transform on genus one fibrations, Noncommutative deformations and flops, Relative integral functors for singular fibrations and singular partners, Relative Fourier–Mukai transforms for Weierstraß fibrations, abelian schemes and Fano fibrations, Fourier-Mukai and autoduality for compactified Jacobians. II, Fourier-Mukai and autoduality for compactified Jacobians. I

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stable sheaves on elliptic fibrations
• Three-dimensional flops and noncommutative rings
• Equivalences of derived categories and \(K3\) surfaces
• Mirror symmetry on K3 surfaces via Fourier-Mukai transform
• \(D\)-equivalence and \(K\)-equivalence
• Flops and derived categories.
• Derived category automorphisms from mirror symmetry
• Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities.
• Homological projective duality
• On a relative Fourier-Mukai transform on genus one fibrations
• Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall 1961. Notes by R. Hartshorne
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Reconstruction of a variety from the derived category and groups of autoequivalences
• Derived categories of twisted sheaves on elliptic threefolds
• Fourier-Mukai transforms for K3 and elliptic fibrations
• Duality between D(X) and with its application to picard sheaves
• Fourier-Mukai transforms for elliptic surfaces
• Equivalences of Triangulated Categories and Fourier-Mukai Transforms
• A Fourier-Mukai Transform for Stable Bundles on K3 Surfaces
• Equivalences of derived categories of sheaves on smooth stacks
• Vector Bundles over Elliptic Fibrations
• The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
• Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstraß cubics
• Complex surfaces with equivalent derived categories