IJPAM: Volume 80, No. 3 (2012)

LINEARLY INDEPENDENT SUBSETS
OF EMBEDDED VARIETIES

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 and non-degenerate variety. Assume $m<n \le 2m+1$. We prove that here is no zero-dimensional scheme $Z\subset X$ witht $\deg (Z) \le 4$ and $\dim (\langle Z )\rangle \le \deg (Z)-2$ and and only if $m=1$, $n=3$ and $X$ is a rational normal curve.

Received: July 14, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: zero-dimensiona scheme, linear dependent zero-dimensional scheme

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3