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arXiv · 2304.07405

Bounding the number of graph refinements for Brill-Noether existence

Karl Christ·Qixiao Ma
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Abstract

Let $G$ be a finite graph of genus $g$. Let $d$ and $r$ be non-negative integers such that the Brill-Noether number is non-negative. It is known that for some $k$ sufficiently large, the $k$-th homothetic refinement $G^{(k)}$ of $G$ admits a divisor of degree $d$ and rank at least $r$. We use results from algebraic geometry to give an upper bound for $k$ in terms of $g,d,$ and $r$.

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Karl Christ, Qixiao Ma. 2023-04-14. Bounding the number of graph refinements for Brill-Noether existence. https://arxiv.org/abs/2304.07405

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