Derived Category Automorphisms from Mirror Symmetry

Abstract

Inspired by the homological mirror symmetry conjecture of Kontsevich, we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth Calabi-Yau variety.

LaTeX, 27 pages, no figures; substantially revised; the erroneous lemma 2.6 has been removed; to appear in the Duke Mathematical Journal

References in corpus (11)

• Phases of $N=2$ Theories In Two Dimensions
• Semiorthogonal decomposition for algebraic varieties
• Hypergeometric functions and mirror symmetry in toric varieties
• A Lie algebra attached to a projective variety
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• Stability conditions on triangulated categories
• Massless D-Branes on Calabi-Yau Threefolds and Monodromy
• Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
• Braid group actions on derived categories of coherent sheaves
• Mirror symmetry and actions of braid groups on derived categories
• Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient

Cited by in corpus (18)

• Dirichlet branes, homological mirror symmetry, and stability
• Derived Categories and Zero-Brane Stability
• D-Brane Stability and Monodromy
• A Point's Point of View of Stringy Geometry
• Massless D-Branes on Calabi-Yau Threefolds and Monodromy
• D-brane categories
• Decompactifications and Massless D-Branes in Hybrid Models
• Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
• Categories of Massless D-Branes and del Pezzo Surfaces
• D-Brane Monodromies, Derived Categories and Boundary Linear Sigma Models
• Fourier Mukai Transforms and Applications to String Theory
• Grassmannian twists on the derived category via spherical functors
• Enhanced gauge symmetry and braid group actions
• Probing Geometry with Stability Conditions
• Mirror Symmetry and Discriminants
• A long exact sequence for symplectic Floer cohomology
• Exoflops in Two Dimensions
• Artin group actions on derived categories of threefolds