Refined Descendant Invariants of Toric Surfaces

Lev Blechman, Eugenii Shustin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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
Issue number1
StatePublished - 15 Jul 2019


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


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


    Dive into the research topics of 'Refined Descendant Invariants of Toric Surfaces'. Together they form a unique fingerprint.

    Cite this