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2014 Derived invariants of irregular varieties and Hochschild homology
Luigi Lombardi
Algebra Number Theory 8(3): 513-542 (2014). DOI: 10.2140/ant.2014.8.513


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.


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Luigi Lombardi. "Derived invariants of irregular varieties and Hochschild homology." Algebra Number Theory 8 (3) 513 - 542, 2014.


Received: 20 September 2012; Revised: 3 June 2013; Accepted: 28 September 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1342.14039
MathSciNet: MR3218801
Digital Object Identifier: 10.2140/ant.2014.8.513

Primary: 14F05

Keywords: equivalences of derived categories , Hochschild homology , Hodge numbers , Picard variety , Rouquier isomorphism , support loci

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.8 • No. 3 • 2014
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