Enumeration of geometric Weierstrass points of metric graphs

2025/06/27 by Diego A. Robayo Bargans, Bargans, Diego A. Robayo
Computer Science · Mathematics · #14T15 #14T20 #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2506.22130

openalex publication_date 2025/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical result states that on a smooth algebraic curve of genus g the number of Weierstrass points, counted with multiplicity, is g³-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 g³-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.

Citations

• Tropical cycles of discrete admissible covers
• A combinatorial extension of tropical cycles
• Catalan-many tropical morphisms to trees; Part I: Constructions
• Specialization of linear systems from curves to graphs
• Tropical curves, their Jacobians and Theta functions
• A Riemann-Roch theorem in tropical geometry
• Riemann-Roch and Abel-Jacobi theory on a finite graph
• The Tropical Grassmannian

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