What question did this study set out to answer?

The aim is to establish a correspondence theorem linking higher genus Gromov-Witten invariants with refined counts of floor diagrams.

March 21, 2026

Refined floor diagrams relative to a conic and Caporaso–Harris‐type formula

Key Points

The aim is to establish a correspondence theorem linking higher genus Gromov-Witten invariants with refined counts of floor diagrams.
Proved a correspondence theorem for higher genus Gromov-Witten invariants with Lambda class insertion.
Developed a recursive Caporaso-Harris-type formula for refining counts of floor diagrams.
Applied the theorem to propose higher genus BPS polynomials for del Pezzo and Hirzebruch surfaces.
Demonstrated a refined correspondence between Gromov-Witten invariants and floor diagrams.
Introduced a recursive formula with potential applications in calculating higher genus polynomials.

Abstract

Abstract We prove a ‐refined correspondence theorem between higher genus relative Gromov–Witten invariants with a Lambda class insertion in the blow‐up of at points on a conic and the refined counts of genus floor diagrams relative to a conic, after the change of variables . We provide a Caporaso–Harris‐type recursive formula for the refined counts of higher genus floor diagrams. As an application of the correspondence theorem, we propose a higher genus version of the BPS polynomials of del Pezzo surfaces of degree and Hirzebruch surfaces, which generalize the higher genus Block–Göttsche polynomials.

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Cite This Study

Ding et al. (Sun,) studied this question.

synapsesocial.com/papers/69be38596e48c4981c678ae9 https://doi.org/https://doi.org/10.1112/jlms.70514

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