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McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

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Abstract

We give a uniform and, to a large extent, geometrical proof that the Poincaré series of the coordinate algebra of a Kleinian singularity and of a Fuchsian singularity of genus 0 is the quotient of the characteristic polynomials of two Coxeter elements. These Coxeter elements are interpreted geometrically, using 2-Calabi-Yau triangulated categories and spherical twist functors.

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Authors and Affiliations

  1. Institut für Algebraische Geometrie, Leibniz Universität Hannover, Postfach 6009, 30060, Hannover, Germany

    Wolfgang Ebeling & David Ploog

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  1. Wolfgang Ebeling
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  2. David Ploog
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Correspondence to Wolfgang Ebeling.

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Ebeling, W., Ploog, D. McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities. Math. Ann. 347, 689–702 (2010). https://doi.org/10.1007/s00208-009-0451-4

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  • DOI: https://doi.org/10.1007/s00208-009-0451-4

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