Welschinger invariants of real Del Pezzo surfaces of degree $\ge 3$

Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin

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arXiv · 1108.3369

Welschinger invariants of real Del Pezzo surfaces of degree $\ge 3$

Ilia Itenberg·Viatcheslav Kharlamov·Eugenii Shustin

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Abstract

We give a recursive formula for purely real Welschinger invariants of real Del Pezzo surfaces of degree $K^2\ge 3$, 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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Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin. 2011-08-16. Welschinger invariants of real Del Pezzo surfaces of degree $\ge 3$. https://arxiv.org/abs/1108.3369

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