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

References in corpus (3)

• Computing Tropical Varieties
• On the tropical Torelli map
• Tropical complexes

Cited by in corpus (8)

• Lefschetz (1,1)-theorem in tropical geometry
• Tropical complexes
• Tropical $\psi$ classes
• Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces
• Riemann-Roch inequality for smooth tropical toric surfaces
• Picard groups for tropical toric schemes
• Excluded homeomorphism types for dual complexes of surfaces
• Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical cycles