Infinitesimal Derived Torelli Theorem for K3 surfaces

Abstract

We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which preserves the Mukai pairing, an infinitesimal weight-2 decomposition and the orientation of a positive 4-dimensional space. This generalizes the derived version of the Torelli Theorem. Along the way we show the compatibility of the actions on Hochschild homology and singular cohomology of any Fourier--Mukai functor.

Main paper by E. Macri and P. Stellari. Appendix by S.Mehrotra. 21 pages. Final version to appear in Int. Math. Res. Not

References in corpus (5)

• Deformation quantization of Poisson manifolds, I
• Derived equivalences of K3 surfaces and orientation
• The relative Riemann-Roch theorem from Hochschild homology
• Non-commutative tori and Fourier-Mukai duality
• The Mukai pairing, I: a categorical approach

Cited by in corpus (8)

• Hodge theory and derived categories of cubic fourfolds
• Derived equivalences of K3 surfaces and orientation
• Derived equivalences of hyperkähler varieties
• Categorical vs topological entropy of autoequivalences of surfaces
• Lefschetz fixed point theorems for Fourier-Mukai functors and DG algebras
• Homogeneity of cohomology classes associated with Koszul matrix factorizations
• Hochschild entropy and Categorical entropy
• Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfaces