Duke Mathematical Journal

Stringy zeta functions for ℚ-Gorenstein varieties

Willem Veys

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Abstract

The stringy Euler number and stringy E-function are interesting invariants of log terminal singularities introduced by Batyrev. He used them to formulate a topological mirror symmetry test for pairs of certain Calabi-Yau varieties and to show a version of the McKay correspondence. It is a natural question whether one can extend these invariants beyond the log terminal case. Assuming the minimal model program, we introduce very general stringy invariants, associated to "almost all" singularities, more precisely, to all singularities that are not strictly log canonical. They specialize to the invariants of Batyrev when the singularity is log terminal. For example, the simplest form of our stringy zeta function is, in general, a rational function in one variable, but it is just a constant (Batyrev's stringy Euler number) in the log terminal case.

Article information

Source
Duke Math. J., Volume 120, Number 3 (2003), 469-514.

Dates
First available in Project Euclid: 16 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1082137352

Digital Object Identifier
doi:10.1215/S0012-7094-03-12031-1

Mathematical Reviews number (MathSciNet)
MR2030094

Zentralblatt MATH identifier
1089.14006

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15] 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45] 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 32S45: Modifications; resolution of singularities [See also 14E15] 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Citation

Veys, Willem. Stringy zeta functions for ℚ-Gorenstein varieties. Duke Math. J. 120 (2003), no. 3, 469--514. doi:10.1215/S0012-7094-03-12031-1. https://projecteuclid.org/euclid.dmj/1082137352


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