IVHS of nodal plane curves

Fuente: arXiv
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Autor principal: Sernesi, Edoardo
Formato: Preprint
Publicado: 2025
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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