论文标题
Hurwitz-Brill-Noether理论中的热带方法
Tropical Methods in Hurwitz-Brill-Noether Theory
论文作者
论文摘要
分裂类型的基因座是曲线的Brill-Noether品种的自然概括，并具有杰出的映射到投影线。我们给出了H. Larson定理的热带证明，表明分裂类型的基因座具有Hurwitz空间一般元素的预期维度。我们的证明使用特定热带曲线系列的分裂类型基因座的明确描述。我们进一步表明，这些热带分裂类型的基因座在Codimension One中连接，并描述一种用于计算其基数时的算法。我们为分裂类型基因座的数值类别提供了一个猜想，我们在许多情况下确认。
Splitting type loci are the natural generalizations of Brill-Noether varieties for curves with a distinguished map to the projective line. We give a tropical proof of a theorem of H. Larson, showing that splitting type loci have the expected dimension for general elements of the Hurwitz space. Our proof uses an explicit description of splitting type loci on a certain family of tropical curves. We further show that these tropical splitting type loci are connected in codimension one, and describe an algorithm for computing their cardinality when they are zero-dimensional. We provide a conjecture for the numerical class of splitting type loci, which we confirm in a number of cases.
