Minimal Lagrangian 2‐Tori in CP 2 Come in Real Families of Every Dimension

It is shown that for every non‐negative integer n , there is a real n ‐dimensional family of minimal Lagrangian tori in CP 2 , and hence of special Lagrangian cones in C 3 whose link is a torus. The proof utilises the fact that such tori arise from integrable systems, and can be described using algebro‐geometric (spectral curve) data.