The embedding dimension of weighted homogeneous surface singularities

Details The embedding dimension of weighted homogeneous surface singularities The embedding dimension of weighted homogeneous surface singularities

2009-10-21

arxiv.org/abs/0910.4035v2

Mathematics

Algebraic Geometry

25 pages, Revised version, to appear in Journal of Topology

Scientific paper

10.1112/jtopol/jtq019

We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the germs is a rational homology sphere. In the case of several sub-families we provide explicit formulas in terms of the Seifert invariants (generalizing results of Wagreich and VanDyke), and we also provide key examples showing that, in general, these invariants are not topological. We extend the discussion to the case of splice--quotient singularities with star--shaped graph as well.

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