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.

arXiv comment34 pages

References in corpus (5)

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• Floor decompositions of tropical curves : the planar case
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• Welschinger invariants of real del Pezzo surfaces of degree $\ge 2$
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Cited by in corpus (11)

• Intersection theory on moduli of disks, open KdV and Virasoro
• Welschinger invariants of real del Pezzo surfaces of degree $\ge 2$
• Relative quantum cohomology
• 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
• A construction of open descendant potentials in all genera
• Frobenius manifolds and quantum groups
• 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