论文标题
图形序列
Gonality sequences of graphs
论文作者
论文摘要
对于任何图，我们将一个称为图形的gonity序列的整数序列关联，该序列由图表上增加等级的最小分隔线组成。这是代数曲线的Gonality序列的热带类似物。我们研究了低属图的高态序列，证明对于属属最高$ 5 $，Gonality序列由该属和第一个Gonity确定。然后，我们证明，通过某些图，可以实现任何合理的前两个gonalities。我们还开发了DHAR的燃烧算法的修改版本，更适合于研究更高的性质。
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.
