Diagrams for Legendrian VMRT

Abstract

We describe varieties of minimal rational tangents on the wonderful symmetric varieties. An irreducible component of a variety of minimal rational tangents is a rational homogeneous space, and hence, we have a corresponding Dynkin diagram expression. On the other hand, we have diagrams from the (marked) Kac diagram of a symmetric space by marking adjacent nodes to the marked node, similar to the case of rational homogeneous spaces. We note that the above two diagrams coincide when the restricted root system is not of type A. This paper is a memo for "minimal rational curves on complete symmetric varieties".Comment: 14pag