# IJPAM: Volume 16, No. 1 (2004)

TRIPLE POINTS AND THE WEAK NON-DEFECTIVITY
OF VERONESE EMBEDDINGS OF
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 , 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.