Combinatorial tropical surfaces

Abstract

We study the combinatorial properties of 2-dimensional tropical complexes. In particular, we prove tropical analogues of the Hodge index theorem and Noether's formula. In addition, we introduce algebraic equivalence for divisors on tropical complexes of arbitrary dimension.

29 pages, 5 figures. This is an expansion of sections 5 and 6 of arXiv:1308.3813v1