An introduction to motivic integration
Abstract
Description
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.
32 pages, 1 figure. Stringy E-function redefined and examples given in more detail. Also we present a proof of the cohomological McKay correspondence for a finite Abelian subgroup of SL(n,C) to illustrate the simplicity of Batyrev's approach in this case
32 pages, 1 figure. Stringy E-function redefined and examples given in more detail. Also we present a proof of the cohomological McKay correspondence for a finite Abelian subgroup of SL(n,C) to illustrate the simplicity of Batyrev's approach in this case