IJPAM: Volume 65, No. 1 (2010)

ZERO-DIMENSIONAL SUBSCHEMES OF A VARIETY $X\subset \mathbb {P}^n$
WHOSE LINEAR SPAN CONTAINS A GIVEN $P\in \mathbb {P}^n$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Fix an integral variety $X\subset \mathbb {P}^n$. Its secant varieties $\sigma _t(X)$ are unions of limits of linear subspaces spanned by reduced subsets of $X$. Here if $X$ is a smooth curve we identify some of these limits using osculating space. Fix $P\in \sigma _t(X)$. We discuss the existence of smoothable zero-dimensional subschemes $Z\subset X$ such that $P\in \langle Z\rangle$ and $\deg (Z)$ is low.

Received: September 23, 2010

AMS Subject Classification: 14N05, 14H99

Key Words and Phrases: secant variety, osculating space, associated space, join, zero-dimensional subscheme

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 1