Gromov–Witten invariants of bielliptic surfaces

Abstract

Bielliptic surfaces appear as a quotient of a product of two elliptic curves and were classified by Bagnera–Franchis. We give a concrete way of computing their GW-invariants with point insertions using a floor diagram algorithm. Using the latter, we are able to prove the quasi-modularity of their generating series by relating them to generating series of graphs for which we also prove quasi-modularity results. We propose a refinement of these invariants by inserting a $\lambda$-class in the considered GW-invariants.