McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

Details McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

2008-09-16

arxiv.org/abs/0809.2738v1

Mathematics

Algebraic Geometry

15 pages, 4 figures

Scientific paper

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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