BPS polynomials and Welschinger invariants

2025/06/03 by Hülya Argüz, Argüz, Hülya, Pierrick Bousseau +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2506.02770

openalex publication_date 2025/06/03 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We generalize Block-Göttsche polynomials, originally defined for toric del Pezzo surfaces, to arbitrary surfaces. To do this, we show that these polynomials arise as special cases of BPS polynomials, defined for any surface S as Laurent polynomials in a formal variable q encoding the BPS invariants of the 3-fold S × ℙ¹. We conjecture that for surfaces S_n obtained by blowing up ℙ² at n general points, the evaluation of BPS polynomials at q=-1 yields Welschinger invariants, given by signed counts of real rational curves. We prove this conjecture for all surfaces S_n with n ≤ 6.

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Cited by

• Refined floor diagrams relative to a conic and Caporaso-Harris type formula

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• On Welschinger invariants of descendant type