IJPAM: Volume 66, No. 4 (2011)

$X\subset \mathbb {P}^n$ MINIMALLY SPANNING 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.Let $X\subset \mathbb {P}^n$ be an integral non-degenerate subvariety. Fix $P\in \mathbb {P}^n$ and an integer $k>0$. Let $\mathcal {Z}(X,P,k)$ (resp. $\mathcal {S}(X,P,k)$) be the set of all zero-dimensional subscheme (resp. zero-dimensional and reduced) $Z\subset X$ such that $\deg (Z)=k$, $P$ is in the linear span $\langle Z\rangle$ of $Z$ but $P\notin \langle Z'\rangle$ for all $Z'\subsetneqq Z$. We study these sets when $X$ is a linearly normal curve with low genus with respect to $n$.

Received: August 2, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: ranks, $X$-rank, zero-dimensional scheme, linearly normal curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4