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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 $g\leq5$ and $\rho(g,r,d)$ 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.

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Atanasov, Stanislav -  Ranganathan, Dhruv - 

Id.: 71041077

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clave14T05 - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 The University of Michigan

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0026-2285
[References] 1945-2365

Fecha de contribución: 17-mar-2018


* Michigan Math. J. 67, iss. 1 (2018), 175-198
* doi:10.1307/mmj/1519095622

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