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arXiv · 2506.11450

Trigonal Curve with Trigonal Deformation of Maximal Rank

Jiacheng Zhang
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Abstract

By extending methods of Favale-Pirola \cite{FavalePirola2022} and Gonz\'{a}lez-Alonso-Torelli\cite{TorelliGonzalezAlonso2024} to toric surfaces via the toric Jacobian ring, we give a computational criterion to determine whether a nondegenerate curve given by ample section of a Hirzebruch surface has first order deformation of rank $g$ within the linear system. We are able to show there exist trigonal curves with trigonal deformations of rank $g$ for $g=2k+1$ and $k\ge 2$ by computing an explicit example.

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Jiacheng Zhang. 2025-06-13. Trigonal Curve with Trigonal Deformation of Maximal Rank. https://arxiv.org/abs/2506.11450

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