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Logarithmic asymptotics of the genus zero Gromov-Witten invariants of the blown up plane.

Itenberg, Ilia; Kharlamov, Viatcheslav; Shustin, Eugenii — 2005

Geometry & Topology

Variétés de Fano réelles

Viatcheslav Kharlamov

Séminaire Bourbaki

Welschinger invariants of small non-toric Del Pezzo surfaces

Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin — 2013

Journal of the European Mathematical Society

We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at $\sim q$ real and $s \leq 1$ pairs of conjugate imaginary points, where $q + 2 s \leq 5$ , and the real quadric blown up at $s \leq 1$ pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil’s recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants of real toric...

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