# American Institute of Mathematical Sciences

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

## Characteristic classes of singular toric varieties

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

Received  October 2013 Revised  November 2013 Published  December 2013

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.
Citation: Laurenţiu Maxim, Jörg Schürmann. Characteristic classes of singular toric varieties. Electronic Research Announcements, 2013, 20: 109-120. doi: 10.3934/era.2013.20.109
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