Motivic Integration, Quotient Singularities and the McKay Correspondence

@article{Denef2002MotivicIQ,
  title={Motivic Integration, Quotient Singularities and the McKay Correspondence},
  author={Jan Denef and François Loeser},
  journal={Compositio Mathematica},
  year={2002},
  volume={131},
  pages={267-290}
}
The present work is devoted to the study of motivic integration on quotient singularities. We give a new proof of a form of the McKay correspondence previously proved by Batyrev. The paper contains also some general results on motivic integration on arbitrary singular spaces. 

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References

SHOWING 1-10 OF 25 REFERENCES

Mirror duality and string-theoretic Hodge numbers

Abstract. We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi–Yau complete intersections in Gorenstein toric Fano varieties. The proof is based on

On the motive of a quotient variety

We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.

Descent, motives and K-theory.

To an arbitrary variety over a field of characteristic zero, we associate a complex of Chow motives, which is, up to homotopy, unique and bounded. We deduce that any variety has a natural Euler

New Trends in Algebraic Geometry: Birational Calabi–Yau n -folds have equal Betti numbers

Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number

Motivic Igusa zeta functions

We define motivic analogues of Igusa's local zeta functions. These functions take their values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta functions and to the

THE TOPOLOGICAL ZETA FUNCTION ASSOCIATED TO A FUNCTION ON A NORMAL SURFACE GERM

Stringy Hodge numbers of varieties with Gorenstein canonical singularities

We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions

La correspondance de McKay

Let M be a quasiprojective algebraic manifold with K_M=0 and G a finite automorphism group of M acting trivially on the canonical class K_M; for example, a subgroup G of SL(n,C) acting on C^n in the

Uniform p-adic cell decomposition and local zeta functions.

The purpose of this paper is to give a cell decomposition for p-adic fields, uniform in p. This generalizes a cell decomposition for fixed p, proved by Denef [7], [9]. We also give some applications