Algebraic Geometry Semina | Minimal rational curves on complete symmetric varieties

We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents, say VMRT. In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves. We relate these results to the restricted root system of the associated symmetric space. In particular, for certain Fano wonderful symmetric varieties, the VMRT has two connected components. Moreover, VMRT is Legandrian when restricted root system is not of type A. This is a joint work with M.Brion and N. Perrin.