Algebraic and combinatorial Brill-Noether theory
Algebraic Geometry
2011-09-28 v2 Combinatorics
Abstract
The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether variety of a graph shown to be non-empty if the Brill-Noether number is non-negative, as a consequence of the analogous fact for smooth projective curves. Similarly, the existence of a graph for which the Brill-Noether variety is empty implies the emptiness of the corresponding Brill-Noether variety for a general curve. The main tool is a refinement of Baker's Specialization Lemma.
Cite
@article{arxiv.1106.1140,
title = {Algebraic and combinatorial Brill-Noether theory},
author = {Lucia Caporaso},
journal= {arXiv preprint arXiv:1106.1140},
year = {2011}
}
Comments
18 pages. 2 figures. Final version incorporating referees comments