Weighted Ehrhart theory and orbifold cohomology

• Autores: Alan Stapledon
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 1, 2008, págs. 63-88
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.04.010
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• Resumen

  • We introduce the notion of a weighted d-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted d-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 d-vector. More specifically, they are sums of dimensions of orbifold cohomology groups of a toric stack