Characteristic classes of singular toric varieties

Laurenţiu Maxim; Jörg Schürmann

doi:10.3934/era.2013.20.109

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2013, Volume 20: 109-120. Doi: 10.3934/era.2013.20.109

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Characteristic classes of singular toric varieties

Laurenţiu Maxim^1, and
Jörg Schürmann^2,

1.
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706
2.
Mathematische Institut, Universität Münster, Einsteinstr. 62, 48149 Münster

Received: September 30, 2013

Revised: October 31, 2013

Published: December 2012

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Abstract

We introduce a new approach for the computation of characteristic classes of singular toric varieties and, as an application, we obtain generalized Pick-type formulae for lattice polytopes. Many of our results (e.g., lattice point counting formulae) hold even more generally, for closed algebraic torus-invariant subspaces of toric varieties. In the simplicial case, by combining this new computation method with the Lefschetz-Riemann-Roch theorem, we give new proofs of several characteristic class formulae originally obtained by Cappell and Shaneson in the early 1990s.

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Mathematics Subject Classification: 14M25, 52B20, 14C17, 14C40.

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