Geometrical description of smooth projective symmetric varieties with Picard number one
Résumé
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.
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