# IJPAM: Volume 10, No. 4 (2004)

SINGULAR HYPERSURFACES OF
INFINITE-DIMENSIONAL PROJECTIVE SPACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract.Fix integers , , an infinite set , a complex Hilbert space with an orthonormal basis equipotent to , and a subset of the set of all hyperplanes of . Assume . Let be the set of all degree complex valued polynomials on . For every fix a closed hyperplane of . Here we prove the existence of an -dimensional linear subspace of not contained in any and such that, setting , is the subset of parametrizing the singular degree hypersurfaces with equations given by .