Bounding the number of graph refinements for Brill-Noether existence

Research output: Working paper/Preprint › Preprint

Authors

  • Karl Christ
  • Qixiao Ma

Research Organisations

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Details

Original languageEnglish
Publication statusE-pub ahead of print - 14 Apr 2023

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 \(r\).

Keywords

    math.AG, math.CO, 05C99 (Primary), 05C57, 14H51 (Secondary)

Cite this

Bounding the number of graph refinements for Brill-Noether existence. / Christ, Karl; Ma, Qixiao.
2023.

Research output: Working paper/Preprint › Preprint

Christ, K., & Ma, Q. (2023). Bounding the number of graph refinements for Brill-Noether existence. Advance online publication.
Christ K, Ma Q. Bounding the number of graph refinements for Brill-Noether existence. 2023 Apr 14. Epub 2023 Apr 14.
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