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

Batyrev, Victor V.. "Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs." Journal of the European Mathematical Society 001.1 (1999): 5-33. <http://eudml.org/doc/277255>.

@article{Batyrev1999,
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.},
author = {Batyrev, Victor V.},
journal = {Journal of the European Mathematical Society},
keywords = {Euler numbers; spaces of arcs of algebraic varieties; orbifold Euler number; stringy Euler number; non-archimedean integration; McKay correspondence; motivic integration; Kawamata log-terminal pair; stringy -function},
language = {eng},
number = {1},
pages = {5-33},
publisher = {European Mathematical Society Publishing House},
title = {Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs},
url = {http://eudml.org/doc/277255},
volume = {001},
year = {1999},
}

TY - JOUR
AU - Batyrev, Victor V.
TI - Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
JO - Journal of the European Mathematical Society
PY - 1999
PB - European Mathematical Society Publishing House
VL - 001
IS - 1
SP - 5
EP - 33
AB - 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.
LA - eng
KW - Euler numbers; spaces of arcs of algebraic varieties; orbifold Euler number; stringy Euler number; non-archimedean integration; McKay correspondence; motivic integration; Kawamata log-terminal pair; stringy -function
UR - http://eudml.org/doc/277255
ER -