The multiple cover formula conjecture for Gromov-Witten invariants of abelian surfaces

Abelian surfaces are complex tori whose enumerative invariants satisfy remarkable regularity properties. The computation of their (reduced) Gromov-Witten invariants for the so called primitive classes is fairly well understood and many complete computations are available. A few years ago, G. Oberdieck conjectured a multiple cover formula expressing in a very simple way the invariants for the non-primitive classes in terms of the primitive one. In this talk, I'll sketch the proof of multiple cover formula conjecture obtained in a joint work with T. Blomme . This effectively solves completely the GW theory of abelian surfaces. The argument relies on a reduced degeneration formula and on the computation of correlated Gromov-Witten invariants for trivial bundles on elliptic curves.