Derived invariants of irregular varieties and Hochschild homology

Lombardi, Luigi

doi:10.2140/ant.2014.8.513

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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

Vol. 8, No. 3, 2014