Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants

We give a tropical description of the counting real log curves in toric degenerations varieties. treat case genus zero and all non-superabundant higher-genus situations. The proof relies on deformation theory is version Nishinou–Siebert approach to correspondence theorem for complex curves. In dimension two, we use similar techniques study with Welschinger signs obtain new Mikhalkin’s invariants.