2010/02/06 by Ilia Itenberg, Itenberg, Ilia, Viatcheslav Kharlamov +3 · 1 citation
Computer Science · Mathematics · #14N10 #14N35 #14P05 #14T05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation
paper · doi:10.48550/arxiv.1002.1399
openalex publication_date 2010/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≤ 1 pairs of conjugate imaginary points, where q+2s≤ 5, and the real quadric blown up at s ≤ 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.