Descendant log Gromov-Witten invariants for toric varieties and tropical curves

Mandel, Travis; Ruddat, Helge

doi:10.1090/tran/7936

Descendant log Gromov-Witten invariants for toric varieties and tropical curves
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by Travis Mandel and Helge Ruddat PDF

Trans. Amer. Math. Soc. 373 (2020), 1109-1152 Request permission

Abstract:

Using degeneration techniques, we prove the correspondence of tropical curve counts and log Gromov-Witten invariants with general incidence and psi-class conditions in toric varieties for genus zero curves. For higher-genus situations, we prove the correspondence for the non-superabundant part of the invariant. We also relate the log invariants to the ordinary ones, in particular explaining the appearance of negative multiplicities in the descendant correspondence result of Mark Gross.

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