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Construction of tropical morphisms from tropical modifications of nonhyperelliptic genus 3 metric graphs with tree gonality 3 to metric trees

2023/01/05 by Hamdi Dërvodeli, Dërvodeli, Hamdi
Computer Science · #Algebraic Geometry (math.AG) #Data Management and Algorithms #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2301.01989

openalex publication_date 2023/01/05 · openalex created_date 2023/01/08 · openalex updated_date 2026/07/28

Abstract

In this article, we look into the tree gonality of genus 3 metric graphs Γ which is defined as the minimum of degrees of all tropical morphisms from any tropical modification of Γ to any metric tree. It is denoted by tgon(Γ) and is at most 3. We define hyperelliptic metric graphs in terms of tropical morphisms and tree gonality. Let Γ be a genus 3 metric graph with tgon(Γ) = 3 which is not hyperelliptic. In this paper, for such metric graphs Γ, we construct a tropical modification Γ' of Γ, a metric tree T and a tropical map φ:Γ' → T of degree 3.

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