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

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.

32 pages, as compared with the published version, a missing deformation label is included (see (DL1), Section 3.3), and an inaccuracy in the proof of Theorem 2 is corrected