IJPAM: Volume 57, No. 4 (2009)

POSTULATION OF DISJOINT UNIONS OF
LINES AND A FIXED SUBSCHEME

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


Abstract.Let $Z \subset \mathbb {P}^n$, $n \ge 5$, be any scheme such that $\dim (Z) \le n-5$. Here we prove the existence of an integer $\alpha _n(Z)$ such that for every integer $y \ge \alpha _n(Z)$ a general union of $Z$ and $y$ lines of $\mathbb {P}^n$ has maximal rank.

Received: October 28, 2009

AMS Subject Classification: 14N05

Key Words and Phrases: unions of lines, Hilbert function, postulation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4