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Tropical descendant Gromov-Witten invariants. (English) Zbl 1171.14039
The authors introduce the tropical version of rational descending Gromov-Witten invariants. These tropical invariants can be computed with a certain lattice path count, similar to G. Mikhalkin’s one [J. Am. Math. Soc. 18, 313–377 (2005; Zbl 1092.14068)], and satisfy a certain WDVV equation (thus being equal to their conventional counterparts under some mild restrictions). This provides a new way to compute descending Gromov-Witten invariants. A similar tropical analogue of descending Gromov-Witten invariants was studied in [M. Gross, Mirror symmetry for $$\mathbb P^2$$ and tropical geometry, preprint arXiv:0903.1378 (2009)].

##### MSC:
 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 14T05 Tropical geometry (MSC2010) 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 14N10 Enumerative problems (combinatorial problems) in algebraic geometry 14H99 Curves in algebraic geometry
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