Trigonal Curve with Trigonal Deformation of Maximal Rank
Abstract
By extending methods of Favale-Pirola arXiv:2108.02157 and Gonz\'alez-Alonso-Torelli arXiv:2402.15158 to toric surfaces via toric Jacobian ring, we are able to show there exists trigonal curve with trigonal deformation of rank g for g=5,7,9,11,13,15 by giving an explicit example. Also, we give a computable criterion to determine whether a nondegenerate ample section of toric surface has first order deformation of rank g within the linear system.
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