%0 Journal Article
%T Vector spaces of skew-symmetric matrices of constant rank
%A Maria Lucia Fania
%A Emilia Mezzetti
%J Mathematics
%D 2010
%I arXiv
%X We study the orbits of vector spaces of skew-symmetric matrices of constant rank 2r and type (N+1)x(N+1) under the natural action of SL(N+1), over an algebraically closed field of characteristic zero. We give a complete description of the orbits for vector spaces of dimension 2, relating them to some 1-generic matrices of linear forms. We also show that, for each rank two vector bundle on P^2 defining a triple Veronese embedding of P^2 in G(1,7), there exists a vector space of 8 x 8 skew-symmetric matrices of constant rank 6 whose kernel bundle is the dual of the given rank two vector bundle.
%U http://arxiv.org/abs/1011.3779v1