Infinitesimal Derived Torelli Theorem for K3 surfaces

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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

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Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/224401

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.2552
 http://arxiv.org/abs/0804.2552

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arXiv