An introduction to motivic integration

Details An introduction to motivic integration An introduction to motivic integration

1999-11-23

arxiv.org/abs/math/9911179v2

Mathematics

Algebraic Geometry

32 pages, 1 figure. Stringy E-function redefined and examples given in more detail. Also we present a proof of the cohomologic

Scientific paper

By associating a `motivic integral' to every complex projective variety X with at worst canonical, Gorenstein singularities, Kontsevich proved that, when there exists a crepant resolution of singularities Y of X, the Hodge numbers of Y do not depend upon the choice of the resolution. In this article we provide an elementary introduction to the theory of motivic integration, leading to a proof of the result described above. We calculate the motivic integral of several quotient singularities and discuss these calculations in the context of the cohomological McKay correspondence.

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