Tropical descendant Gromov-Witten invariants
Hannah Markwig, Johannes Rau

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.
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