Enumeration of geometric Weierstrass points of metric graphs

Fuente: arXiv
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Autore principale: Bargans, Diego A. Robayo
Natura: Preprint
Pubblicazione: 2025
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author Bargans, Diego A. Robayo
author_facet Bargans, Diego A. Robayo
contents 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 $2$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_22130
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Enumeration of geometric Weierstrass points of metric graphs
Bargans, Diego A. Robayo
Combinatorics
Algebraic Geometry
14T15, 14T20
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 $2$.
title Enumeration of geometric Weierstrass points of metric graphs
topic Combinatorics
Algebraic Geometry
14T15, 14T20
url https://arxiv.org/abs/2506.22130