IVHS of nodal plane curves

Abstract

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 $\pi$ has maximal variation if and only if $\pi = 0$.