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Motivic integration for some varieties with a torus action

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KAH - K-theory, algebraic cycles and motivic homotopy theory

Motivic integration was introduced by Kontsevich in 1995 and has proved useful in birational geometry and singularity theory. It assigns to constructible subsets of the arc space of a variety a “volume” which takes values in the Grothendieck ring of algebraic varieties, and it behaves in many ways just like usual integration. I will explain how motivic integration can be used to compute Batyrev's “stringy invariants”, which are a generalization of Hodge numbers to singular varieties, for a family of varieties with a torus action. A potential application is to the study of mirror symmetry for these varieties. (Joint with K. Langlois and M. Raibaut.)




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