AI 中文总结
该研究确定了一大类环面上固定几何亏格一般整曲线的Scrollar不变量，推广了Castryck与Cools的组合公式，描述了预期行为并给出了其在部分Severi簇不可约分支失效的例子。
AI 中文摘要
给定环面上的一条曲线，单项式投影会诱导出从该曲线的正规化到射影直线的映射。我们针对一大类环面上具有固定几何亏格的一般整曲线，确定了相关的Scrollar不变量，这推广了Castryck与Cools在特征零下针对光滑曲线计算此类Scrollar不变量的组合公式。我们描述了任意环面情形下的预期行为，但提供了相应Severi簇的至少某个不可约分支上该行为失效的例子。
英文摘要
Given a curve on a toric surface, a monomial projection induces a map from the normalization of the curve to the projective line. We determine the associated scrollar invariants for general integral curves of fixed geometric genus for a large class of toric surfaces. This generalizes a combinatorial formula to calculate such scrollar invariants for smooth curves in characteristic zero due to Castryck and Cools. We describe an expected behaviour for any toric surface, but provide examples where this fails at least on some irreducible component of the corresponding Severi variety.
