We define a series of relative tropical Welschinger-type invariants of real toric surfaces. In the Del Pezzo case, these invariants can be seen as real tropical analogs of relative Gromov–Witten invariants, and are subject to a recursive formula. As application we obtain new formulas for Welschinger invariants of real toric Del Pezzo surfaces.
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Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin, A Caporaso–Harris type formula for Welschinger invariants of real toric Del Pezzo surfaces. Comment. Math. Helv. 84 (2009), no. 1, pp. 87–126DOI 10.4171/CMH/153