IJPAM: Volume 18, No. 4 (2005)

ON THE NON-DEFECTIVITY AND
NON WEAK-DEFECTIVITY OF SEGRE-VERONESE
EMBEDDINGS OF PRODUCTS OF ${\bf {P}}^n\times {\bf {P}}^m$

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 $n, m, d, t$ such that $n \ge m \ge 1$, $n \ge 2$, $d \ge n!(n+1)-n$ and $t \ge mn+1$. Here we prove that the Segre-Veronese embedding of ${\bf {P}}^n\times {\bf {P}}^m$ induced by the complete linear system $\vert \mathcal {O}_{{\bf {P}}^n\times {\bf {P}}^m} \vert$ is neither defective nor weakly defective.

Received: January 5, 2005

AMS Subject Classification: 14N05

Key Words and Phrases: secant variety, Segre embedding, Veronese embedding, Horace Lemma, zero-dimensional scheme

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 4