Infinitesimal Derived Torelli Theorem for K3 surfaces
Algebraic Geometry
2009-03-25 v2
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.
Cite
@article{arxiv.0804.2552,
title = {Infinitesimal Derived Torelli Theorem for K3 surfaces},
author = {Emanuele Macri and Paolo Stellari and Sukhendu Mehrotra},
journal= {arXiv preprint arXiv:0804.2552},
year = {2009}
}
Comments
Main paper by E. Macri and P. Stellari. Appendix by S.Mehrotra. 21 pages. Final version to appear in Int. Math. Res. Not