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 (VMRT). In particular, we prove that these varieties are homogeneous and that for non-exceptional indecomposable wonderful varieties, there is a unique family of minimal rational curves, and hence a unique VMRT. We relate these results to the restricted root system of the associated symmetric space.