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 ‐class in the considered GW‐invariants.