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