IVHS of nodal plane curves

2025/12/13 by Edoardo Sernesi, Sernesi, Edoardo
Mathematics · #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2512.12316

openalex publication_date 2025/12/13 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

Let \V_d,n be the Severi variety of irreducible plane curves of degree d≥ 4 having n nodes, with 0≤ n ≤ \binomd-12-1. We prove that for every [\ol C]∈ \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 ≥ 1 mapping with degree d ≥ 2 to a fixed curve Y of genus π has maximal variation if and only if π= 0.

Citations

• Maximal variation of linear systems
• General infinitesimal variations of Hodge structure of ample curves in surfaces
• Remarks on the positivity of the cotangent bundle of a K3 surface
• Equigeneric and equisingular families of curves on surfaces
• Koszul complexes and pole order filtrations

Related

• Linear sections of the Severi variety and moduli of curves
• On plane maximal curves
• Geometry of families of nodal curves on rational surfaces
• Computing Node Polynomials for Plane Curves
• On maximal plane curves of degree 3 over \mathbbF₄,and Sziklai's example of degree q-1 over \mathbbF_q