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

Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

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

, Volume 1 (1) – Jan 1, 1999
29 pages

/lp/springer-journals/non-archimedean-integrals-and-stringy-euler-numbers-of-log-terminal-Al00NI3UNP
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/PL00011158
Publisher site
See Article on Publisher Site

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.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Jan 1, 1999