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Remarks on derived equivalences of Ricci-flat manifolds

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Dec 2009Embargo end date: 01 Jan 2008 Germany Publisher:Springer Science and Business Media LLCJournal:Mathematische Zeitschrift, volume 267, pages 939-963 (issn: 0025-5874, eissn: 1432-1823,

Authors: Huybrechts, Daniel; Nieper-Wißkirchen, Marc A.;

doi: 10.1007/s00209-009-0655-z , 10.48550/arxiv.0801.4747

arXiv: http://arxiv.org/abs/0801.4747

Remarks on derived equivalences of Ricci-flat manifolds

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Abstract

We present results indicating that the decomposition of a Ricci-flat manifold in its irreducible factors is reflected by the derived category of coherent sheaves. More precisely, we prove that a smooth projective variety that is derived equivalent to an abelian variety resp. an irreducible symplectic variety is of the same type. The paper also contains a proof of a conjecure of Caldararu for manifolds with trivial canonical bundle saying that the modified HKR isomorphism for Hochschild homology is compatible with the module structure.

25 pages

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Germany

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Mathematics - Algebraic Geometry, 14J32, FOS: Mathematics, 18E30, Algebraic Geometry (math.AG), 14J32; 18E30

1 Research products, page 1 of 1

The module structure of Hochschild homology in some examples
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