Vector spaces of skew-symmetric matrices of constant rank - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: We study the orbits of vector spaces of skew-symmetric matrices of constantrank 2r and type N+1xN+1 under the natural action of SLN+1, over analgebraically closed field of characteristic zero. We give a completedescription of the orbits for vector spaces of dimension 2, relating them tosome 1-generic matrices of linear forms. We also show that, for each rank twovector bundle on P^2 defining a triple Veronese embedding of P^2 in G1,7,there exists a vector space of 8 x 8 skew-symmetric matrices of constant rank 6whose kernel bundle is the dual of the given rank two vector bundle.



Author: Maria Lucia Fania, Emilia Mezzetti

Source: https://arxiv.org/







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