Projective normality of the wonderful compactification of semisimple adjoint groups

Abstract.

We prove that if G is a semisimple adjoint group over an algebraically closed field of arbitrary characteristic, X is the wonderful compactification of G and $\widehat{G}$ is a simply connected covering of G, then for any $\widehat{G}\times \widehat{G}$-linearised very ample line bundle L over X, the cone over X given by L is normal.