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arXiv · 2506.22130

Enumeration of geometric Weierstrass points of metric graphs

Diego A. Robayo Bargans
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Abstract

A classical result states that on a smooth algebraic curve of genus $g$ the number of Weierstrass points, counted with multiplicity, is $g^3-g$. In this paper, we introduce the notion of geometric Weierstrass points of metric graphs and show that a generic metric graph of genus $g$ has $g^3-g$ geometric Weierstrass points counted with multiplicity. Our methods also provide a new proof of the existence of Weierstrass points on metric graphs of genus bigger than or equal to $2$.

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Diego A. Robayo Bargans. 2025-06-27. Enumeration of geometric Weierstrass points of metric graphs. https://arxiv.org/abs/2506.22130

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