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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received March 19, 1998
Rights and permissions
About this article
Cite this article
Batyrev, V. Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs . J. Eur. Math. Soc. 1, 5–33 (1999). https://doi.org/10.1007/PL00011158
Issue Date:
DOI: https://doi.org/10.1007/PL00011158