Derived invariants of irregular varieties and Hochschild homology

Details Derived invariants of irregular varieties and Hochschild homology Derived invariants of irregular varieties and Hochschild homology

2012-04-05

arxiv.org/abs/1204.1332v2

Mathematics

Algebraic Geometry

37 pages

Scientific paper

We study the behavior of cohomological support loci of the canonical bundle under derived equivalence of smooth projective varieties. This is achieved by investigating the derived invariance of a generalized version of Hochschild homology. Furthermore, using techniques coming from birational geometry, we establish the derived invariance of the Albanese dimension for varieties having non-negative Kodaira dimension. We apply our machinery to study the derived invariance of the holomorphic Euler characteristic and of certain Hodge numbers for special classes of varieties. Further applications concern the behavior of particular types of fibrations under derived equivalence.

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