Log homogeneous compactifications of some classical groups

Mathieu Huruguen (1)

1 Department of Mathematics [New York]

We generalize in positive characteristics some results of Bien and Brion on log homogeneous compactifications of a homogeneous space under the action of a connected reductive group. We also construct an explicit smooth log homogeneous compactification of the general linear group by successive blow-ups starting from a grassmannian. By taking fixed points of certain involutions on this compactification, we obtain smooth log homogeneous compactifications of the special orthogonal and the symplectic groups.

Mots clés: spherical varieties; log homogeneous compactifications; canonical compactifications; wonderful compactifications

Domaines: Géométrie algébrique [math.AG]

Mathieu Huruguen. Log homogeneous compactifications of some classical groups. 2013. ⟨hal-00808098⟩