Generators of modules in tropical geometry

Abstract

A module $M$ over the tropical semifield $T$ is analogous to a module over a field. We assume that $M$ is straight reflexive, and define the dimension of $M$ to the number of elements of a basis. We study the dimension of a straight reflexive submodule $N\subset M$. Also we find an enough condition to the reflexivity. This result has an application to polytopes in a tropical projective space, and also to a Riemann-Roch theorem for tropical curves.

36 pages, introduction is changed

References in corpus (1)

• The Maslov dequantization, idempotent and tropical mathematics: A brief introduction

Cited by in corpus (3)

• The Riemann-Roch strategy, Complex lift of the Scaling Site
• On tropical Clifford's Theorem
• Riemann-Roch inequality for smooth tropical toric surfaces