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

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

2011-08-16

arxiv.org/abs/1108.3369v2

Mathematics

Algebraic Geometry

32 pages, minor corrections, to appear in Math. Annalen

Scientific paper

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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