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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2009
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/0910.4035 |
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| _version_ | 1866917145296764928 |
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| author | Némethi, András Okuma, Tomohiro |
| author_facet | Némethi, András Okuma, Tomohiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0910_4035 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | The embedding dimension of weighted homogeneous surface singularities Némethi, András Okuma, Tomohiro Algebraic Geometry 14B05, 32S25, 14J17 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. |
| title | The embedding dimension of weighted homogeneous surface singularities |
| topic | Algebraic Geometry 14B05, 32S25, 14J17 |
| url | https://arxiv.org/abs/0910.4035 |