IJPAM: Volume 2, No. 2 (2002)

CLOSED ORBITS FOR ACTIONS OF
INFINITE-DIMENSIONAL LINEAR GROUPS

E. Ballico
Dept. of Mathematics
University of Trento
38050 Povo (Trento) - Via Sommarive 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $V$ be an infinite-dimensional locally convex topological vector space. For any $d\ge 2$ the projective linear group $PGL(V)$ acts on the set of all degree $d$ hypersurfaces of ${\bf {P}}(V)$. Here we determine the unique closed orbit for this action and the good orbits whose closure is the union of two orbits.

Received: April 16, 2002

AMS Subject Classification: 20G99, 32K05, 58B12, 14C05, 14N05

Key Words and Phrases: infinite-dimensional projective space, infinite-dimensional Grassmannian, flag variety, hypersurface, projective linear group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 2