Analysis of the Brill-Noether game on metric cactus graphs
Jorn van der Pol
A metric graph is a metric realisation of a weighted discrete graph. We
investigate the existence of winning strategies in a certain chip-firing game
on metric cactus graphs, i.e. metric realisations of discrete cactus graphs. We
link the Brill-Noether game to the concept of linear systems of divisors on
metric graphs. Existence of winning strategies is then implied by Brill-Noether
theory on algebraic curves and recent work by Matthew Baker, linking linear
systems on algebraic curves to linear systems on metric graphs v.v., an
argument which uses sophisticated algebraic geometry. We provide a new
elementary proof of the existence of winning strategies.