Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 16 (2006), No. 1, 039--046Copyright Heldermann Verlag 2006 On Exceptional Completions of Symmetric Varieties Rocco Chirivì Dip. di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy chirivi@dm.unipi.it Andrea Maffei Dip. di Matematica, Università di Roma "La Sapienza", P.le Aldo Moro 5, 00185 Roma, Italy amaffei@mat.uniroma1.it [Abstract-pdf] Let $G$ be a simple group with an exceptional involution $\sigma$ having $H$ as fixed point set. We study the embedding of $G/H$ in the projective space ${\mathbb P}(V)$ for a simple $G$--module $V$ with a line fixed by $H$ but having no nonzero vector fixed by $H$. For a certain class of such modules $V$ we describe the closure of $G/H$ proving in particular that it is a smooth variety. Keywords: Complete symmetric variety, exceptional involution. MSC: 14M17, 14L30 [ Fulltext-pdf  (162  KB)] for subscribers only.