IJPAM: Volume 88, No. 1 (2013)

RANKS OF LINEAR SUBSPACES WITH
RESPECT TO AN EMBEDDED VARIETY

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let $X\subset \mathbb {P}^r$ be an integral and non-degenerate variety and $V\subset \mathbb {P}^r$ a $k$-dimensional linear subspace. For any $P\in \mathbb {P}^r$ the $X$-rank of $P$ is the minimal cardinality of a subset of $X$ whose linear span contains $P$. Here we study several integers related to the $X$-rank of $V$, e.g. the minimal $X$-rank of all elements of a basis of $V$ or the minimal sum of the $X$-ranks of a basis of $V$.

Received: June 11, 2013

AMS Subject Classification: 14H99, 14N05

Key Words and Phrases: X-rank, linear subspace, Grassmannian

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DOI: 10.12732/ijpam.v88i1.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 1