Combinatorial tropical surfaces

2015/06/05 by Dustin Cartwright, Cartwright, Dustin · 3 citations
Computer Science · Engineering · Mathematics · #14T05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CO #msc:14T05

paper · pdf · doi:10.48550/arxiv.1506.02023

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

arxiv created 2015/06/05 · openalex publication_date 2015/06/05 · arxiv updated 2015/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces
• Picard groups for tropical toric schemes
• Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical\n cycles

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