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arXiv · 2511.10327

Conic linear series and pencils of plane quartics

Riccardo Moschetti·Gian Pietro Pirola·Lidia Stoppino
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Abstract

We study linear systems cut out by cones of fixed degree on a smooth complex curve $C\subset\mathbb{P}^{3}$. 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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Riccardo Moschetti, Gian Pietro Pirola, Lidia Stoppino. 2025-11-13. Conic linear series and pencils of plane quartics. https://arxiv.org/abs/2511.10327

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