TY - JOUR
T1 - Refined Descendant Invariants of Toric Surfaces
AU - Blechman, Lev
AU - Shustin, Eugenii
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/7/15
Y1 - 2019/7/15
N2 - 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.
AB - 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.
KW - Gromov–Witten invariants
KW - Moduli spaces of tropical curves
KW - Tropical curves
KW - Tropical descendant invariants
KW - Tropical enumerative geometry
UR - http://www.scopus.com/inward/record.url?scp=85064613372&partnerID=8YFLogxK
U2 - 10.1007/s00454-019-00093-y
DO - 10.1007/s00454-019-00093-y
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AN - SCOPUS:85064613372
SN - 0179-5376
VL - 62
SP - 180
EP - 208
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 1
ER -