Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces

2018/09/28 by Ken Sumi, Sumi, Ken
Computer Science · Mathematics · Medicine · #14C40 #14T05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cancer Treatment and Pharmacology #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1809.10987

openalex publication_date 2018/09/28 · openalex created_date 2018/10/05 · openalex updated_date 2026/08/01

Abstract

We show that the space of theta functions on tropical tori is identified with a convex polyhedron. We also show a Riemann-Roch inequality for tropical abelian surfaces by calculating the self-intersection numbers of divisors.

Citations

• Combinatorial tropical surfaces
• Tropical Geometry and its applications

Related

• Riemann-Roch inequality for smooth tropical toric surfaces
• Tropical curves, their Jacobians and Theta functions
• A Riemann-Roch theorem in tropical geometry
• Tropical theta characteristics
• The complement of tropical curves in moderate position on tropical surfaces