Riemann-Roch inequality for smooth tropical toric surfaces

TL;DR

This paper establishes a Riemann-Roch inequality for smooth tropical toric surfaces by defining new estimative measures for the dimension of global sections of divisors, facilitating easier computation.

Contribution

It introduces two new measures to estimate $h^{0}(X,D)$ and proves a Riemann-Roch inequality for smooth tropical toric surfaces, advancing tropical geometry theory.

Findings

Established a Riemann-Roch inequality for smooth tropical toric surfaces

Defined two new quantities to estimate $h^{0}(X,D)$

Provided a method for easier computation of global sections

Abstract

For a divisor $D$ on a tropical variety $X$, we define two amounts in order to estimate the value of $h^{0}(X,D)$, which are described by terms of global sections and computed more easily than $h^{0}(X,D)$. As an application of its estimation, we show that a Riemann-Roch inequality holds for smooth tropical toric surfaces.