Integration over Tropical Plane Curves and Ultradiscretization

TL;DR

This paper explores the relationship between holomorphic integrals on tropical plane curves and ultradiscretization, demonstrating that lattice integrals on tropical curves can be derived as limits of complex integrals on Riemann surfaces.

Contribution

It establishes a connection between tropical geometry and complex analysis by showing how lattice integrals on tropical curves emerge from limits of classical complex integrals.

Findings

Lattice integrals over tropical curves are limits of complex integrals on Riemann surfaces.

Provides a method to study tropical integrals via classical complex analysis.

Bridges the gap between tropical geometry and ultradiscretization techniques.

Abstract

In this article we study holomorphic integrals on tropical plane curves in view of ultradiscretization. We prove that the lattice integrals over tropical curves can be obtained as a certain limit of complex integrals over Riemannian surfaces.