Abstract
We give a recursive formula for purely real Welschinger invariants of real Del Pezzo surfaces of degree K 2 ≥ 3, where in the case of surfaces of degree 3 with two real components we introduce a certain modification of Welschinger invariants and enumerate exclusively the curves traced on the non-orientable component. As an application, we prove the positivity of the invariants under consideration and their logarithmic asymptotic equivalence, as well as congruence modulo 4, to genus zero Gromov–Witten invariants.
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Itenberg, I., Kharlamov, V. & Shustin, E. Welschinger invariants of real Del Pezzo surfaces of degree ≥ 3. Math. Ann. 355, 849–878 (2013). https://doi.org/10.1007/s00208-012-0801-5
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DOI: https://doi.org/10.1007/s00208-012-0801-5