Shin-Young Kim, [T-seminar] Wonderful Symmetric Varieties and their Varieties of Minimal Rational Tangents II

As a general background, we talk about adjoint symmetric varieties and their wonderful compactification. We describe the families of minimal rational curves on wonderful symmetric varieties corresponding to varieties of minimal rational tangents (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, and hence a unique VMRT. After, we list varieties of minimal rational tangents of wonderful symmetric varieties using a marked diagram when the restricted root system is not A-type. This is based on the work “Minimal rational curves on complete symmetric varieties” with Michel Brion and Nicolas Perrin.