IJPAM: Volume 70, No. 4 (2011)

SUBSCHEMES OF A VERONESE EMBEDDING OF
THE PLANE WHOSE LINEAR SPAN MEET

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


Abstract. Let $X_{2,d} \subset \mathbb {P}^{\binom{d+2}{2}-1}$ be the order $d$ Veronese embedding of $\mathbb {P}^2$. We give a necessary and sufficient condition for the existence of schemes $Z, W\subset X_{2,d}$ and $P\in \langle Z\rangle \cap \langle W\rangle$ such that $Z\cap W = \emptyset$ and $P$ is not contained in the linear span of a scheme strictly contained in either $Z$ or $W$.

Received: November 5, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: $X$-rank, Veronese embedding, Veronese surface, 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: 2011
Volume: 70
Issue: 4