Tropical descendant Gromov–Witten invariants

By Hannah Markwig, Johannes Rau. 2008

56 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/7adc254d1cf45361f182dd99d14cc30b48234f98

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Descendant log Gromov-Witten invariants for toric varieties and tropical curves (2016, background): “ proper. By absence of automorphisms, the two spaces in the top row are actually schemes. If all of our ψ-classes are associated with point conditions (as is the case for the situations considered in [MR09] and [Rau15]), then the correspondence theorem for products of projective spaces reads as foll”
On the tropical Torelli map (2009, background): “For instance, this program has been carried out successfully for many problems of real and complex enumerative geometry, see for example [32,40,50,24,25,11,33,7,21].”