Welschinger invariants of real Del Pezzo surfaces of degree ≥ 3

Ilia Itenberg (1) , Viatcheslav Kharlamov (2) , Eugenii Shustin (3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IRMA - Institut de Recherche Mathématique Avancée
3 TAU - School of Mathematical Sciences [Tel Aviv]

We give a recursive formula for purely real Welschinger invariants of real Del Pezzo surfaces of degree K 2 ≥ 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.

Domaines: Géométrie algébrique [math.AG]

Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin. Welschinger invariants of real Del Pezzo surfaces of degree ≥ 3. Mathematische Annalen, 2013, 355 (3), ⟨10.1007/s00208-012-0801-5⟩. ⟨hal-01295175⟩