A minimal resolution for the Jacobian ideal of a generic curve arrangement
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916886483042304 |
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| author | Dimca, Alexandru Sticlaru, Gabriel |
| author_facet | Dimca, Alexandru Sticlaru, Gabriel |
| contents | We consider a nodal curve $C$ in the complex projective plane whose irreducible components $C_i$ are smooth. A minimal set of generators $G$ for the first and second syzygy modules of the Jacobian ideal of $C$ are described, using recent results by Th. Kahle, H. Schenck, B. Sturmfels and M. Wiesmann on the likelihood correspondence. The elements of $G$ have explicit formulas in terms of the equations $f_i=0$ of the irreducible components $C_i$ of $C$. Similar results, including extensions to hypersurfaces arrangements in $\mathbb{P}^n$ were obtained by R. Burity, Z. Ramos, A. Simis and St. Toh\u aneanu with a genericity assumption which may not be easy to test in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A minimal resolution for the Jacobian ideal of a generic curve arrangement Dimca, Alexandru Sticlaru, Gabriel Algebraic Geometry Commutative Algebra We consider a nodal curve $C$ in the complex projective plane whose irreducible components $C_i$ are smooth. A minimal set of generators $G$ for the first and second syzygy modules of the Jacobian ideal of $C$ are described, using recent results by Th. Kahle, H. Schenck, B. Sturmfels and M. Wiesmann on the likelihood correspondence. The elements of $G$ have explicit formulas in terms of the equations $f_i=0$ of the irreducible components $C_i$ of $C$. Similar results, including extensions to hypersurfaces arrangements in $\mathbb{P}^n$ were obtained by R. Burity, Z. Ramos, A. Simis and St. Toh\u aneanu with a genericity assumption which may not be easy to test in practice. |
| title | A minimal resolution for the Jacobian ideal of a generic curve arrangement |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2508.04439 |