Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity

2001/09/26 by Wolfgang Ebeling, Ebeling, Wolfgang
Mathematics · #13D40 (Primary) 20C15 (Secondary) #14J17 #32S25 #32S40 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13D40 #msc:14J17 #msc:20C15 #msc:32S25 #msc:32S40

paper · pdf · doi:10.48550/arxiv.math/0109210

LaTeX2e, 12 pages

arxiv created 2001/09/26 · arxiv updated 2009/11/30

Abstract

A relation is proved between the Poincaré series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. For a Kleinian singularity not of type A_2n, this amounts to the statement that the Poincaré series is the quotient of the characteristic polynomial of the Coxeter element by the characteristic polynomial of the affine Coxeter element of the corresponding root system. We show that this result also follows from the McKay correspondence.

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