Refined Descendant Invariants of Toric Surfaces

Lev Blechman, Eugenii Shustin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We construct refined tropical enumerative genus zero invariants of toric surfaces that specialize to the tropical descendant genus zero invariants introduced by Markwig and Rau when the quantum parameter tends to 1. In the case of trivalent tropical curves our invariants turn to be the Göttsche–Schroeter refined broccoli invariants. We show that this is the only possible refinement of the Markwig–Rau descendant invariants that generalizes the Göttsche–Schroeter refined broccoli invariants. We discuss also the computational aspect (a lattice path algorithm) and exhibit some examples.

Original languageEnglish
Pages (from-to)180-208
Number of pages29
JournalDiscrete and Computational Geometry
Volume62
Issue number1
DOIs
StatePublished - 15 Jul 2019

Funding

FundersFunder number
German?Israeli Foundation
German–Israeli Foundation1174-197.6/2011
École Normale Supérieure
Israel Science Foundation501/18, 176/15
Max-Planck-Gesellschaft

    Keywords

    • Gromov–Witten invariants
    • Moduli spaces of tropical curves
    • Tropical curves
    • Tropical descendant invariants
    • Tropical enumerative geometry

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