IVHS of nodal plane curves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909959942307840 |
|---|---|
| author | Sernesi, Edoardo |
| author_facet | Sernesi, Edoardo |
| contents | Let $\V_{d,n}$ be the Severi variety of irreducible plane curves of degree $d\ge 4$ having $n$ nodes, with $0\le n \le \binom{d-1}{2}-1$. We prove that for every $[\ol C]\in \V_{d,n}$, the infinitesimal variation of the Hodge structure of the normalization $C$ of $\ol C$ is maximal as $[\ol C]$ moves in $\V_{d,n}$. As a preliminary result, we also prove that the family of curves of genus $g \ge 1$ mapping with degree $d \ge 2$ to a fixed curve $Y$ of genus $π$ has maximal variation if and only if $π= 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | IVHS of nodal plane curves Sernesi, Edoardo Algebraic Geometry 14H10 Let $\V_{d,n}$ be the Severi variety of irreducible plane curves of degree $d\ge 4$ having $n$ nodes, with $0\le n \le \binom{d-1}{2}-1$. We prove that for every $[\ol C]\in \V_{d,n}$, the infinitesimal variation of the Hodge structure of the normalization $C$ of $\ol C$ is maximal as $[\ol C]$ moves in $\V_{d,n}$. As a preliminary result, we also prove that the family of curves of genus $g \ge 1$ mapping with degree $d \ge 2$ to a fixed curve $Y$ of genus $π$ has maximal variation if and only if $π= 0$. |
| title | IVHS of nodal plane curves |
| topic | Algebraic Geometry 14H10 |
| url | https://arxiv.org/abs/2512.12316 |