Riemann-Roch inequality for smooth tropical toric surfaces

2021/05/25 by Ken Sumi, Sumi, Ken
Computer Science · Mathematics · #Polynomial and algebraic computation #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2105.12216

Abstract

For a divisor D on a tropical variety X, we define two amounts in order to estimate the value of h⁰(X,D), which are described by terms of global sections and computed more easily than h⁰(X,D). As an application of its estimation, we show that a Riemann-Roch inequality holds for smooth tropical toric surfaces.

Related

• Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces
• A Riemann-Roch theorem in tropical geometry
• Refined elliptic tropical invariants of toric surfaces
• The complement of tropical curves in moderate position on tropical surfaces
• On tropical Clifford's Theorem