# Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs

### Victor V. Batyrev

Universität Tübingen, Germany

## 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.

## Cite this article

Victor V. Batyrev, Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. J. Eur. Math. Soc. 1 (1999), no. 1, pp. 5–33

DOI 10.1007/PL00011158