Spaces of matrices of constant rank and uniform vector bundles

2015/08/02 by Philippe Ellia, Ellia, Philippe, Paolo Menegatti +1
Mathematics · #14J60 #15A30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J60 #msc:15A30

paper · pdf · doi:10.48550/arxiv.1508.00209

12 pages

arxiv created 2015/08/02 · arxiv updated 2015/08/04

Abstract

Let A be a k-vector space of dimension a. A subvector space M of End(A) is said to be of rank r if every non-zero f in M has rank r. The problem considered in this paper is to determine l(r;a) the maximal dimension of a rank r subspace of End(A). Known results are reviewed in the language of vector bundles. Some new results are proved and a conjecture is made.

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