Algebraic and combinatorial Brill-Noether theory

Understand

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.