Commentarii Mathematici Helvetici


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Volume 84, Issue 1, 2009, pp. 87–126
DOI: 10.4171/CMH/153

Published online: 2009-03-31

A Caporaso–Harris type formula for Welschinger invariants of real toric Del Pezzo surfaces

Ilia Itenberg[1], Viatcheslav Kharlamov[2] and Eugenii Shustin[3]

(1) Université de Strasbourg, France
(2) Université de Strasbourg, France
(3) Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv, Israel

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.

Keywords: Tropical curves, enumerative geometry, Welschinger invariants, Caporaso–Harris formula, toric surfaces

Itenberg Ilia, Kharlamov Viatcheslav, Shustin Eugenii: A Caporaso–Harris type formula for Welschinger invariants of real toric Del Pezzo surfaces. Comment. Math. Helv. 84 (2009), 87-126. doi: 10.4171/CMH/153