IJPAM: Volume 63, No. 3 (2010)

ON THE $X$-RANKS OF TANGENT VECTORS OF CURVES
AND VERONESE EMBEDDINGS OF ARBITRARY VARIETIES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X\subset \mathbb {P}^n$, $n \ge 4$, be a smooth curve of genus $\ge 2$. Let $\tau (X)$ be the tangent developable of $X$. Fix a general $P\in \tau (X)$. Here we prove the non-existence of $S\subset X$ such that $\sharp (S)=2$ and $P\in \langle S \rangle$. We prove a similar result for Veronese embeddings of order $\ge 3$ of arbitrary varieties.

Received: April 22, 2010

AMS Subject Classification: 14N05, 14H50

Key Words and Phrases: ranks, tangent developable of a curve, Veronese embedding, multiprojective space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 3