McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities
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چکیده
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.
منابع مشابه
Poincaré series and Coxeter functors for Fuchsian singularities
We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincaré series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the lattices and isometries involved, lifting them to triangulated categories.
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تاریخ انتشار 2008