Journal of the European Mathematical Society


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Volume 1, Issue 1, 1999, pp. 5–33
DOI: 10.1007/PL00011158

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

Victor V. Batyrev[1]

(1) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, TÜBINGEN, GERMANY

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.

Keywords: Euler numbers, spaces of arcs of algebraic varieties

Batyrev Victor: Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. J. Eur. Math. Soc. 1 (1999), 5-33. doi: 10.1007/PL00011158