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.

Vector spaces of skew-symmetric matrices of constant rank

FANIA, Maria Lucia;
2011-01-01

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/23449
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