Alastair Craw
Published 1999-11-23, updated 2001-09-27Version 2
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.
Comments: 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
Motivic integration, quotient singularities and the McKay correspondence
Beyond twisted maps:~applications to motivic integration
The space of curvettes of quotient singularities and associated invariants
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