2025/06/13 by Jiacheng Zhang, Zhang, Jiacheng
#math.AG
paper · pdf · doi:10.48550/arxiv.2506.11450
By extending methods of Favale-Pirola \citeFavalePirola2022 and González-Alonso-Torelli\citeTorelliGonzalezAlonso2024 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≥ 2 by computing an explicit example.