The embedding dimension of weighted homogeneous surface singularities
arXiv:0910.4035 · doi:10.1112/jtopol/jtq019
Abstract
We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincaré 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.
25 pages, Revised version, to appear in Journal of Topology
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- Complete intersection singularities of splice type as universal abelian covers
- The geometric genus of splice-quotient singularities
- Seiberg-Witten invariants and surface singularities II. Singularities with good $\C^*$-action
- The cohomology of line bundles of splice-quotient singularities