Tohoku Mathematical Journal
2006

December
SECOND SERIES VOL. 58, NO. 4

Tohoku Math. J.
58 (2006), 599-616

Title ON NORMALITY OF CONES OVER SYMMETRIC VARIETIES

Author Rocco Chirivì, Corrado De Concini and Andrea Maffei

(Received May 25, 2005, revised April 24, 2006)
Abstract. Let $G$ be a simply connected semisimple algebraic group and let $K$ be the subgroup of points fixed by an involution of $G$. For certain representations containing a line $r$ preserved by $K$, we study the normality of the closure of the set of vectors which are $G$ conjugate to a vector in $r$. Some applications of our result to the normality of certain classical varieties are given.

2000 Mathematics Subject Classification. Primary 14M17; Secondary 14L30.

Key words and phrases. Complete symmetric variety, projective normality.

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