Gonality Sequences of Graphs
Gonality Sequences of Graphs
复制标题
图的调性序列
DOI：
10.1137/20m1323072
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Julie Yuan
中科院分区：
文献类型：
--
作者：
Ivan Aidun;Frances Dean;Ralph Morrison;Teresa Yu;Julie Yuan
对于任何一个图，我们关联一个整数序列，称为图的角性序列，由图上的递增秩的因子的最小度组成。这是一个热带模拟的gonality序列的代数曲线。研究了低亏格图的角度序列，证明了亏格不超过5的图的角度序列是由亏格和第一角度决定的。然后，我们证明了任何合理的对前两个角是由一些图。我们还开发了一个修改版本的达尔的燃烧算法更适合于研究更高的gonalities。
To any graph we associate a sequence of integers called the gonality sequence of the graph, consisting of the minimum degrees of divisors of increasing rank on the graph. This is a tropical analogue of the gonality sequence of an algebraic curve. We study gonality sequences for graphs of low genus, proving that for genus up to $5$, the gonality sequence is determined by the genus and the first gonality. We then prove that any reasonable pair of first two gonalities is achieved by some graph. We also develop a modified version of Dhar's burning algorithm more suited for studying higher gonalities.