On the Jacobian Scheme of a plane curve
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909095966015488 |
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| author | Canino, Stefano Gimigliano, Alessandro Idà, Monica |
| author_facet | Canino, Stefano Gimigliano, Alessandro Idà, Monica |
| contents | We study the Jacobian scheme of a plane algebraic curve at an ordinary singularity, characterizing it through a geometric property. We compute the Tjurina number for a family of curves at an ordinary singularity showing that it reaches the minimum possible value, using very elementary methods, essentially Gröbner basis. We give an algorithm that gives the analytic type of a double point using the algebraic version of the Mather-Yau Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Jacobian Scheme of a plane curve Canino, Stefano Gimigliano, Alessandro Idà, Monica Algebraic Geometry 14B05, 14H20 We study the Jacobian scheme of a plane algebraic curve at an ordinary singularity, characterizing it through a geometric property. We compute the Tjurina number for a family of curves at an ordinary singularity showing that it reaches the minimum possible value, using very elementary methods, essentially Gröbner basis. We give an algorithm that gives the analytic type of a double point using the algebraic version of the Mather-Yau Theorem. |
| title | On the Jacobian Scheme of a plane curve |
| topic | Algebraic Geometry 14B05, 14H20 |
| url | https://arxiv.org/abs/2302.07042 |