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

Asaf Horev; Jake P. Solomon

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

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arxiv 1210.4034 v1 pith:NCO234SL submitted 2012-10-15 math.SG hep-thmath.AG

Asaf Horev , Jake P. Solomon This is my paper · ORCID

classification math.SGhep-thmath.AG

keywords invariantsblowupsopenplaneprojectivealgorithmanaloguesarbitrary

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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.

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BPS polynomials and Welschinger invariants
math.AG 2025-06 conditional novelty 7.0 of 10

The new BPS polynomials of surfaces specialize at q=-1 to Welschinger invariants for blowups of the projective plane at up to six points.

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