an:07174515
Zbl 1442.14166
Mandel, Travis; Ruddat, Helge
Descendant log Gromov-Witten invariants for toric varieties and tropical curves
EN
Trans. Am. Math. Soc. 373, No. 2, 1109-1152 (2020).
00447132
2020
j
14M25 14N10 14N35 14T15
tropical Gromov-Witten; Psi class insertion
The authors study genus zero, as well as higher genus Gromov-Witten invariants (in non-superabundant situations) of smooth toric varieties with Psi-class conditions. The main result shows that the tropical description of such invariants coincides with the classical one. The technique that is used to show this correspondence builds on the approach of \textit{T. Nishinou} and \textit{B. Siebert} [Duke Math. J. 135, No. 1, 1--51 (2006; Zbl 1105.14073)]. In particular, it uses logarithmic Gromov-Witten theory and toric degenerations. The authors also allow incidence conditions in the toric boundary for applications to non-toric situations. Moreover, tropically they study arbitrary tropical cycles as incidence conditions, not just affine linear ones as in Nishinou-Siebert.
Hulya Arguz (London)
Zbl 1105.14073