McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

Abstract

We give a conceptual 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 triangulated categories and spherical twist functors.

arXiv comment15 pages, 4 figures

References in corpus (2)

• Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity
• The Poincaré series of some special quasihomogeneous surface singularities