The special Lagrangian torus fibration conjecture for the projective plane

Let $D\subset\mathbb{CP}^2$ be a smooth elliptic curve, and equip $\mathbb{CP}^2\setminus D$ with the holomorphic volume form having poles along $D$. Special Lagrangian torus fibration conjecture for $\mathbb{CP}^2$. The complement carries a special Lagrangian torus fibration over a disc with, generically, three nodal singular fibers. This is the basic two-dimensional example motivating the later double-cover constructions; the source indicates that the general deformation argument for an arbitrary cubic had not yet been proved.