## Minimal rational curves on wonderful group compactifications

### Baohua Fu

Let *G* be a simple algebraic group of adjoint type, and *V* an irreducible projective representation. The closure of the image of *G* in the projectivization of End(*V*) is an equivariant compactification *X*(*V*) of the group *G*. We answer the following questions: Is *X*(*V*) covered by lines? If not, what is the minimal degree of a family of rational curves covering *X*(*V*), and what is the structure of such a family? In particular, one may find *V* such that *X*(*V*) is covered by lines, except when *G* has type E_{8}. The combinatorics of the highest short coroot play an important role in these questions. This is a joint work with Michel Brion.