Bounding the number of graph refinements for Brill-Noether existence
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918428562948096 |
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| author | Christ, Karl Ma, Qixiao |
| author_facet | Christ, Karl Ma, Qixiao |
| contents | 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 $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07405 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounding the number of graph refinements for Brill-Noether existence Christ, Karl Ma, Qixiao Algebraic Geometry Combinatorics 05C99 (Primary), 05C57, 14H51 (Secondary) 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 $r$. |
| title | Bounding the number of graph refinements for Brill-Noether existence |
| topic | Algebraic Geometry Combinatorics 05C99 (Primary), 05C57, 14H51 (Secondary) |
| url | https://arxiv.org/abs/2304.07405 |