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Non-Archimedian integrals and stringy Euler numbers of log terminal pairs

Victor V. Batyrev
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Abstract

Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log terminal pairs. There is a natural Kawamata log terminal pair corresponding to an algebraic variety V having a regular action of a finite group G. In this situation we show that the stringy Euler number of this pair coincides with the physicists' orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten formula. As an application, we prove a conjecture of Miles Reid on the Euler numbers of crepant desingularizations of Gorenstein quotient singularities.

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Victor V. Batyrev. 1998-03-16. Non-Archimedian integrals and stringy Euler numbers of log terminal pairs. https://arxiv.org/abs/math/9803071

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