Vol. 8, No. 3, 2014
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Derived invariants of irregular varieties and Hochschild homology

Luigi Lombardi
Vol. 8 (2014), No. 3, 513–542
DOI: 10.2140/ant.2014.8.513
Abstract

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 nonnegative 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.

Keywords
equivalences of derived categories, support loci, Hochschild homology, Hodge numbers, Picard variety, Rouquier isomorphism
Mathematical Subject Classification 2010
Primary: 14F05
Milestones
Received: 20 September 2012
Revised: 3 June 2013
Accepted: 28 September 2013
Published: 31 May 2014
Authors
Luigi Lombardi
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
53115 Bonn
Germany