The open Gromov-Witten-Welschinger theory of blowups of the projective plane

Abstract

We compute the Welschinger invariants of blowups of the projective plane at an arbitrary conjugation invariant configuration of points. Specifically, open analogues of the WDVV equation and Kontsevich-Manin axioms lead to a recursive algorithm that reconstructs all the invariants from a small set of known invariants. Example computations are given, including the non-del Pezzo case.

34 pages

References in corpus (2)

• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Welschinger invariants of small non-toric Del Pezzo surfaces

Cited by in corpus (4)

• On higher genus Welschinger invariants of Del Pezzo surfaces
• Fixed-point Localization for ${\mathbb{RP}}^{2m}\subset {\mathbb{CP}}^{2m}$
• Welschinger invariants of Blow-ups of symplectic 4-manifolds
• An Introduction to ${\mathbf{A}}^1$-Enumerative Geometry