Lifting matroid divisors on tropical curves
© Cartwright. 2015
Received: 25 February 2015
Accepted: 11 September 2015
Published: 10 November 2015
Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves realizing this bound might only exist over certain characteristics or over certain fields of definition. Our examples also apply to the theory of metrized complexes and weighted graphs. These examples arise by relating the lifting problem to matroid realizability. We also give a proof of Mnëv universality with explicit bounds on the size of the matroid, which may be of independent interest.