Counting (tropical) curves via scattering.sage

TL;DR

This paper introduces a method to compute relative Gromov-Witten invariants of pairs using scattering diagrams, supported by a tropical correspondence theorem and demonstrated through examples and Sage code implementation.

Contribution

It presents a novel computational approach linking scattering diagrams with tropical geometry for non-toric cases of Gromov-Witten invariants.

Findings

Successful computation of examples using the method

Development of Sage code for scattering diagram calculations

Validation of the tropical correspondence theorem in non-toric settings

Abstract

In this note I will explain how relative/log Gromov-Witten invariants of pairs $(X,D)$ with very ample smooth anticanonical divisor $D$ can be computed using algebro-combinatorial objects called scattering diagrams. The underlying principle behind this computational method is a tropical correspondence theorem for non-toric cases, which I will explain briefly. By computing some examples I will give an introduction to a sage code that I wrote for computing scattering diagrams.