| The 10-dimensional moduli space of rational curves of degree 3 on a general cubic fourfold Y admits a contraction M--> Z to an 8-dimensional projective symplectic manifold. This contains the original fourfold Y as a Lagrangian subvariety. An explicit calculation shows that Z has the same Euler number as Hilb^4(K3). This is joint work with C. Sorger, D. van Straten and C. Lehn |