Tropical descendant Gromov-Witten invariants

TL;DR

This paper introduces tropical Psi-classes on the moduli space of rational tropical curves in R^2, proving their intersection properties and providing an algorithm to count such curves, linking tropical and classical enumerative geometry.

Contribution

It defines tropical Psi-classes, establishes a WDVV equation, and generalizes Mikhalkin's lattice path algorithm for counting tropical curves with specific conditions.

Findings

Tropical Psi-classes satisfy a WDVV equation.

Tropical curve counts match classical enumerative invariants.

An algorithm for counting tropical curves with Psi- and evaluation conditions is presented.

Abstract

We define tropical Psi-classes on the moduli space of rational tropical curves in R^2 and consider intersection products of Psi-classes and pull-backs of evaluations on this space. We show a certain WDVV equation which is sufficient to prove that tropical numbers of curves satisfying certain Psi- and evaluation conditions are equal to the corresponding classical numbers. We present an algorithm that generalizes Mikhalkin's lattice path algorithm and counts rational plane tropical curves satisfying certain Psi- and evaluation conditions.