The distribution of Weierstrass points on a tropical curve

David Harry Richman
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Abstract

We show that on a metric graph of genus g, a divisor of degree \(n\) generically has \(g(n-g+1)\) Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass points become distributed according to the Zhang canonical measure. In other words, the limiting distribution is determined by effective resistances on the metric graph. This distribution result has an analogue for complex algebraic curves, due to Neeman, and for curves over non-Archimedean fields, due to Amini.

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热带曲线上魏尔斯特拉斯点的分布
我们证明,在属 g 的度量图上,度数为 \(n\) 的除数一般具有 \(g(n-g+1)\)魏尔斯特拉斯点。对于度数增长到无穷大的公元图上的一般除数序列,我们证明相关的魏尔斯特拉斯点会按照张规范度量分布。换句话说,极限分布是由公元图上的有效阻力决定的。这一分布结果类似于尼曼(Neeman)提出的复代数曲线,也类似于阿米尼(Amini)提出的非阿基米德域上的曲线。
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