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arXiv · 0809.2738

McKay correspondence for the Poincar\'e series of Kleinian and Fuchsian singularities

Wolfgang Ebeling·David Ploog
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Abstract

We give a conceptual proof that the Poincar\'e 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 triangulated categories and spherical twist functors.

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Wolfgang Ebeling, David Ploog. 2008-09-16. McKay correspondence for the Poincar\'e series of Kleinian and Fuchsian singularities. https://arxiv.org/abs/0809.2738

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