, Volume 129, Issue 3, pp 293-335,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 17 Mar 2009

Tropical descendant Gromov–Witten invariants

Abstract

We define tropical Psi-classes on \({\mathcal{M}_{0,n}(\mathbb{R}^2, d)}\) 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.

The first author is supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.