Clifford representatives via the uniform algebraic rank
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908391975157760 |
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| author | Barbosa, Myrla Christ, Karl Melo, Margarida |
| author_facet | Barbosa, Myrla Christ, Karl Melo, Margarida |
| contents | In this paper, we introduce the uniform algebraic rank of a divisor class on a finite graph. We show that it lies between Caporaso's algebraic rank and the combinatorial rank of Baker and Norine. We prove the Riemann-Roch theorem for the uniform algebraic rank, and show that both the algebraic and the uniform algebraic rank are realized on effective divisors. As an application, we use the uniform algebraic rank to show that Clifford representatives always exist. We conclude with an explicit description of such Clifford representatives for a large class of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clifford representatives via the uniform algebraic rank Barbosa, Myrla Christ, Karl Melo, Margarida Algebraic Geometry Combinatorics In this paper, we introduce the uniform algebraic rank of a divisor class on a finite graph. We show that it lies between Caporaso's algebraic rank and the combinatorial rank of Baker and Norine. We prove the Riemann-Roch theorem for the uniform algebraic rank, and show that both the algebraic and the uniform algebraic rank are realized on effective divisors. As an application, we use the uniform algebraic rank to show that Clifford representatives always exist. We conclude with an explicit description of such Clifford representatives for a large class of graphs. |
| title | Clifford representatives via the uniform algebraic rank |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2406.03987 |