Conic linear series and pencils of plane quartics

2025/11/13 by Riccardo Moschetti, Gian Pietro Pirola, Moschetti, Riccardo +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Holomorphic and Operator Theory #math.AG

paper · pdf · doi:10.48550/arxiv.2511.10327

openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28

Abstract

We study linear systems cut out by cones of fixed degree on a smooth complex curve C⊂ℙ³. We develop a systematic study of the families of such systems, considering their limits, their infinitesimal behaviour and some associated geometric structures. As an application, we prove the existence of a non-isotrivial pencil of quartics with only one base point, all whose members are irreducible and whose general member is smooth.

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