IJPAM: Volume 16, No. 1 (2004)
OF VERONESE EMBEDDINGS OF
PROJECTIVE SPACES
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it
Abstract.Fix integers , and such that
and general points
. Let
(resp.
) denote the projective space
of all degree hypersurfaces of singular at each point ,
, (resp.
singular at each and with a triple point at ). Here we use Horace Method to prove
that
,
and (in characteristic zero) a general
satisfies
and it has an ordinary node at each . This result implies that the order Veronese embedding of
is not weakly -defective in the sense of Ciliberto and Chiantini.
Received: July 5, 2004
AMS Subject Classification: 14N05
Key Words and Phrases: Veronese variety, weakly defective variety, zero-dimensional scheme, double point, fat point, Veronese embedding
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 1