Geometrical description of smooth projective symmetric varieties with Picard number one

Alessandro Ruzzi (1)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

In [A. Ruzzi, Smooth projective symmetric varieties with Picard number equal to one, Int. J. Math., to appear] we have classied the smooth projective symmetric G-varieties with Picard number one (and G semisimple). In this paper we give a geometrical description of such varieties. In particular, we determine their automorphism group. When this group acts nontransitively on X, we describe a G-equivariant embedding of the variety X in a homogeneous variety (with respect to a larger group). We show that these varieties are all related to the exceptional groups.

Mots clés: Symmetric varieties; Fano varieties

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Alessandro Ruzzi. Geometrical description of smooth projective symmetric varieties with Picard number one. Transformation Groups, 2010, 15 (1), pp.201-226. ⟨10.1007/s00031-010-9074-9⟩. ⟨hal-00576033v2⟩