Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T03:19:07.677Z Has data issue: false hasContentIssue false

ON THE CONCEPT OF k-SECANT ORDER OF A VARIETY

Published online by Cambridge University Press:  24 April 2006

LUCA CHIANTINI
Affiliation:
Dipartimento di Scienze Matematiche e Informatiche, Università di Siena, Pian dei Mantellini 44, 53100 Siena, [email protected]
CIRO CILIBERTO
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, [email protected]
Get access

Abstract

For a variety X of dimension n in ${\mathbb P}^r,\ r\geq n(k+1)+k$, the kth secant order of X is the number $\mu_k(X)$ of $(k+1)$-secant k-spaces passing through a general point of the kth secant variety. We show that, if $r>n(k+1)+k$, then $\mu_k(X)=1$ unless X is k-weakly defective. Furthermore we give a complete classification of surfaces $X\subset{\mathbb P}^r,\ r>3k+2$, for which $\mu_k(X)>1$.

Keywords

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)