Remarks on derived equivalences of Ricci-flat manifolds

Daniel Huybrechts; Marc Nieper-Wisskirchen

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arXiv · 0801.4747

Remarks on derived equivalences of Ricci-flat manifolds

Daniel Huybrechts·Marc Nieper-Wisskirchen

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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.

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Daniel Huybrechts, Marc Nieper-Wisskirchen. 2008-01-30. Remarks on derived equivalences of Ricci-flat manifolds. https://arxiv.org/abs/0801.4747

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