Tropical vertex and real enumerative geometry

TL;DR

This paper links the algebraic structure of the refined tropical vertex group to the enumeration of real rational curves in toric surfaces, revealing a deep connection between algebraic relations and geometric counting.

Contribution

It establishes a novel correspondence between commutator relations in the tropical vertex group and real enumerative geometry in toric surfaces.

Findings

Commutator relations can be expressed through real rational curve counts.

Provides a new geometric interpretation of algebraic structures in tropical geometry.

Bridges algebraic and geometric perspectives in enumerative problems.

Abstract

We show that the commutator relations in the refined tropical vertex group can be expressed via the enumeration of suitable real rational curves in toric surfaces.