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 (7)

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• A construction of open descendant potentials in all genera
• Welschinger invariants of Blow-ups of symplectic 4-manifolds
• Relative quantum cohomology of the Chiang Lagrangian
• An Introduction to ${\mathbf{A}}^1$-Enumerative Geometry
• Open WDVV Equations and Frobenius Structures for Toric Calabi-Yau 3-Folds