# Tropical refined curve counting from higher genera and lambda classes

## TL;DR

This paper reveals that Block-G"ottsche's tropical curve counts, refined by a q-number, correspond to generating series of higher genus log Gromov-Witten invariants with lambda class insertions, providing geometric insight and invariance.

## Contribution

It establishes a direct link between tropical refined curve counts and higher genus log Gromov-Witten invariants, clarifying their geometric meaning and invariance.

## Key findings

- Block-G"ottsche invariants correspond to higher genus log Gromov-Witten invariants
- The q-refinement encodes deformation invariance
- Provides a geometric interpretation of tropical curve counts

## Abstract

Block and G\"ottsche have defined a $q$-number refinement of counts of tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we show that the result is a generating series of higher genus log Gromov-Witten invariants with insertion of a lambda class. This gives a geometric interpretation of the Block-G\"ottsche invariants and makes their deformation invariance manifest.