Curves contained in a quartic determinantal surface containing a line

Abel Castorena; Montserrat Vite

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arXiv · 2606.27303

Curves contained in a quartic determinantal surface containing a line

Abel Castorena·Montserrat Vite

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Abstract

Let $X\subseteq \mathbb{P}^{3}$ be a very general element of the Noether-Lefschetz divisor that parametrizing smooth quartic surfaces containing a line. Let $L\subseteq X$ denote the corresponding line. We study the curves contained in $X$ and analyze their behavior in the Hilbert scheme. We first determine which linear systems contain smooth irreducible curves. For most classes, we verify that the general member is a smooth point of the expected Hilbert scheme. Finally we compute the Rao function of any curve on $X$.

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Abel Castorena, Montserrat Vite. 2026-06-25. Curves contained in a quartic determinantal surface containing a line. https://arxiv.org/abs/2606.27303

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