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

Journal of the European Mathematical Society (1999)

- Volume: 001, Issue: 1, page 5-33
- ISSN: 1435-9855

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topBatyrev, 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 -

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