Minimal rational curves on wonderful group compactifications

Michel Brion (1) , Baohua Fu (2)

1 IF - Institut Fourier
2 AMSS - Academy of Mathematics and Systems Science

Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an application, we show that X has the target rigidity property when G is not of type A_1 or C.

Domaines: Géométrie algébrique [math.AG]

Michel Brion, Baohua Fu. Minimal rational curves on wonderful group compactifications. Journal de l'École polytechnique — Mathématiques, 2015, 2, pp.153-170. ⟨hal-01622770⟩