Duke Mathematical Journal

Stringy zeta functions for ℚ-Gorenstein varieties

Willem Veys

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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

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

First available in Project Euclid: 16 April 2004

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Zentralblatt MATH identifier

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]


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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