The Poincaré series of some special quasihomogeneous surface singularities

Details The Poincaré series of some special quasihomogeneous surface singularities The Poincaré series of some special quasihomogeneous surface singularities

2000-04-13

arxiv.org/abs/math/0004086v3

Mathematics

Algebraic Geometry

LaTeX2e, 17 pages, 2 figures; rewritten; only part of the old preprint; other part rewritten as ''Poincar\'{e} series and mono

Scientific paper

In the author's paper ''Poincar\'{e} series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity'' a relation is proved between the Poincar\'{e} series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. We study this relation for Fuchsian singularities and show that it is connected with the mirror symmetry of K3 surfaces and with automorphisms of the Leech lattice. We also indicate relations between other singularities and Conway's group.

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