Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants
arXiv:2004.05124 · doi:10.5802/aif.3507
Abstract
We give a tropical description of the counting of real log curves in toric degenerations of toric varieties. We treat the case of genus zero curves and all non-superabundant higher-genus situations. The proof relies on log deformation theory and is a real version of the Nishinou-Siebert approach to the tropical correspondence theorem for complex curves. In dimension two, we use similar techniques to study the counting of real log curves with Welschinger signs and we obtain a new proof of Mikhalkin's tropical correspondence theorem for Welschinger invariants.
v2: 65 pages, 15 figures. Revised version, published in Annales de l'Institut Fourier. arXiv admin note: text overlap with arXiv:math/0409060 by other authors
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