Residues and Gorenstein Contractions of Genus One Curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916831531368448 |
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| author | Neff, Adrian Wise, Jonathan |
| author_facet | Neff, Adrian Wise, Jonathan |
| contents | Let $C$ be a genus one nodal curve over a local artinian base and let $E$ be a proper subcurve of genus one. We define residues for curves over local artinian rings, then define generalized residues with values in line bundles over the local artinian ring that arise from tropical data on the curve. We then use these residues to construct a contraction of $C$ that collapses $E$ to a Gorenstein genus one singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Residues and Gorenstein Contractions of Genus One Curves Neff, Adrian Wise, Jonathan Algebraic Geometry Let $C$ be a genus one nodal curve over a local artinian base and let $E$ be a proper subcurve of genus one. We define residues for curves over local artinian rings, then define generalized residues with values in line bundles over the local artinian ring that arise from tropical data on the curve. We then use these residues to construct a contraction of $C$ that collapses $E$ to a Gorenstein genus one singularity. |
| title | Residues and Gorenstein Contractions of Genus One Curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.05326 |