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arXiv · 1201.2104

Integration on Artin toric stacks and Euler characteristics

Dan Edidin·Yogesh More
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Abstract

There is a well developed intersection theory on smooth Artin stacks with quasi-affine diagonal. However, for Artin stacks whose diagonal is not quasi-finite the notion of the degree of a Chow cycle is not defined. In this paper we propose a definition for the degree of a cycle on Artin toric stacks whose underlying toric varieties are complete. As an application we define the Euler characteristic of an Artin toric stack with complete good moduli space - extending the definition of the orbifold Euler characteristic. An explicit combinatorial formula is given for 3-dimensional Artin toric stacks.

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Dan Edidin, Yogesh More. 2012-01-10. Integration on Artin toric stacks and Euler characteristics. https://arxiv.org/abs/1201.2104

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