Poincaré series and Coxeter functors for Fuchsian singularities

Details Poincaré series and Coxeter functors for Fuchsian singularities Poincaré series and Coxeter functors for Fuchsian singularities

2009-03-26

arxiv.org/abs/0903.4692v1

Mathematics

Algebraic Geometry

11 pages, 1 figure

Scientific paper

We consider Fuchsian singularities of arbitrary genus and prove, in a
conceptual manner, a formula for their Poincar\'e 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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