论文标题
所有三角曲线的精制布里尔·纳特理论
Refined Brill-Noether theory for all trigonal curves
论文作者
论文摘要
三角曲线提供了Brill-Noether特殊曲线的示例。 [9]的定理1.3表征了一般三角曲线的Brill-Noether理论和Brill-Noether裂片基因座的精制分层，该基因座的线条捆绑捆绑包，其向前推向$ \ Mathbb {p}^1 $具有指定的分布类型。本说明描述了所有三角曲线的精制分层。鉴于三角曲线的Maroni不变，我们确定了所有Brill-Noether分裂基因座的尺寸，并描述其不可减至的成分。当尺寸为正时，这些基因座是连接的，如果Maroni不变性为$ 0 $或$ 1 $，则它们是不可约的。
Trigonal curves provide an example of Brill-Noether special curves. Theorem 1.3 of [9] characterizes the Brill-Noether theory of general trigonal curves and the refined stratification by Brill-Noether splitting loci, which parametrize line bundles whose push forward to $\mathbb{P}^1$ has a specified splitting type. This note describes the refined stratification for all trigonal curves. Given the Maroni invariant of a trigonal curve, we determine the dimensions of all Brill-Noether splitting loci and describe their irreducible components. When the dimension is positive, these loci are connected, and if furthermore the Maroni invariant is $0$ or $1$, they are irreducible.
