Weighted Ehrhart Theory and Orbifold Cohomology

Details Weighted Ehrhart Theory and Orbifold Cohomology Weighted Ehrhart Theory and Orbifold Cohomology

2007-11-28

arxiv.org/abs/0711.4382v6

Adv. Math. 219 (2008), 63-88.

Mathematics

Combinatorics

23 pages. Final copy, minor changes, to appear in Adv. Math

Scientific paper

We introduce the notion of a weighted $\delta$-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted $\delta$-vectors from a combinatorial perspective. We present a version of Ehrhart Reciprocity and prove a change of variables formula. We deduce a new geometric interpretation of the coefficients of the Ehrhart $\delta$-vector. More specifically, they are sums of dimensions of orbifold cohomology groups of a toric stack.

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