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- W2963938135 abstract "In an influential 2008 paper, Baker proposed a number of conjectures relating the Brill–Noether theory of algebraic curves with a divisor theory on finite graphs. In this note, we examine Baker’s Brill–Noether existence conjecture for special divisors. For g≤5 and ρ(g,r,d) nonnegative, every graph of genus g is shown to admit a divisor of rank r and degree at most d. As further evidence, the conjecture is shown to hold in rank 1 for a number families of highly connected combinatorial types of graphs. In the relevant genera, our arguments give the first combinatorial proof of the Brill–Noether existence theorem for metric graphs, giving a partial answer to a related question of Baker." @default.
- W2963938135 created "2019-07-30" @default.
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- W2963938135 date "2018-03-01" @default.
- W2963938135 modified "2023-09-25" @default.
- W2963938135 title "A Note on Brill–Noether Existence for Graphs of Low Genus" @default.
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- W2963938135 doi "https://doi.org/10.1307/mmj/1519095622" @default.
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