manuscripta mathematica

, Volume 129, Issue 3, pp 293–335

Tropical descendant Gromov–Witten invariants

Open AccessArticle

DOI: 10.1007/s00229-009-0256-5

Cite this article as:
Markwig, H. & Rau, J. manuscripta math. (2009) 129: 293. doi:10.1007/s00229-009-0256-5

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.

Mathematics Subject Classification (2000)

Primary 14N3552B20
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© The Author(s) 2009

Authors and Affiliations

  1. 1.Courant Research Center “Higher Order Structures in Mathematics”Georg-August-Universität GöttingenGöttingenGermany
  2. 2.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany