The Euler number of the Jacobi factor of a plane curve singularity whose semigroup is $\langle4,6,13\rangle$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866914719051284480 |
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| author | Watari, Masahiro |
| author_facet | Watari, Masahiro |
| contents | Piontkowski calculated the Euler number of Jacobi factors of plane curve singularities with semigroups $< p, q>$, $< 4, 2q, s>$, $< 6,8,s>$ and $< 6,10, s>$. %His analysis was done by decomposing the Jacobi factors into affine cells. In this paper, we show that a Jacobi factor for any curve singularity admits a cell decomposition by virtue of Pfister and Steenbrink's theory for punctual Hilbert schemes. We also introduce a computational method to determine the number of affine cells in the decomposition. Applying it, we compute the the Euler number of the Jacobi factor of a singularity with a semigroup $< 4,6,13>$. Our result gives a counterexample for Piontkowski's calculation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1310_2781 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | The Euler number of the Jacobi factor of a plane curve singularity whose semigroup is $\langle4,6,13\rangle$ Watari, Masahiro Algebraic Geometry Piontkowski calculated the Euler number of Jacobi factors of plane curve singularities with semigroups $< p, q>$, $< 4, 2q, s>$, $< 6,8,s>$ and $< 6,10, s>$. %His analysis was done by decomposing the Jacobi factors into affine cells. In this paper, we show that a Jacobi factor for any curve singularity admits a cell decomposition by virtue of Pfister and Steenbrink's theory for punctual Hilbert schemes. We also introduce a computational method to determine the number of affine cells in the decomposition. Applying it, we compute the the Euler number of the Jacobi factor of a singularity with a semigroup $< 4,6,13>$. Our result gives a counterexample for Piontkowski's calculation. |
| title | The Euler number of the Jacobi factor of a plane curve singularity whose semigroup is $\langle4,6,13\rangle$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1310.2781 |