2016/02/29 by Lev Blechman, Eugenii Shustin · 1 citation
Mathematics · #math.AG #msc:14N10 #msc:14T05
paper · pdf · doi:10.1007/s00454-019-00093-y
published as Discrete and Computational Geometry (2019) · 30 pages, 7 figures; matches the published version
arxiv created 2019/05/08 · arxiv updated 2019/05/09
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 Goettsche-Schroeter refined broccoli invariants. We show that this is the only possible refinement of the Markwig-Rau descendant invariants that generalizes the Goettsche-Schroeter refined broccoli invariants. We discuss also the computational aspect (a lattice path algorithm) and exhibit some examples.