Geodesic
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
Journal of the European Mathematical Society, Tome 1 (1999) no. 1, pp. 5-33

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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.
DOI : 10.1007/pl00011158
Classification : 14-XX, 32-XX, 58-XX, 00-XX
Keywords: Euler numbers, spaces of arcs of algebraic varieties 
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     title = {Non-Archimedean integrals and stringy {Euler} numbers of log-terminal pairs},
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Victor V. Batyrev. Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. Journal of the European Mathematical Society, Tome 1 (1999) no. 1, pp. 5-33. doi: 10.1007/pl00011158

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