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arXiv · 1002.1399

Welschinger invariants of small non-toric Del Pezzo surfaces

Ilia Itenberg·Viatcheslav Kharlamov·Eugenii Shustin
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Abstract

We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at $q$ real and $s \leq 1$ pairs of conjugate imaginary points, where $q+2s\le 5$, 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 for Gromov-Witten invariants of these surfaces and generalizes our recursive formula for purely real Welschinger invariants of real toric Del Pezzo surfaces. As a consequence, we prove the positivity of the Welschinger invariants under consideration and their logarithmic asymptotic equivalence to genus zero Gromov-Witten invariants.

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Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin. 2011-08-10. Welschinger invariants of small non-toric Del Pezzo surfaces. https://arxiv.org/abs/1002.1399

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