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On linear spaces of skew-symmetric matrices of constant rank

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Abstract

Motivated by the study of congruences of lines, we consider linear systems of skew-symmetric matrices of order six and constant rank four. We prove that, up to projective automorphisms, there exist exactly four types of such linear systems of dimension two, giving four families all of the same dimension.

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Authors and Affiliations

  1. Institut Fourier, UMR 5582 (UJF-CNRS), BP 74, 38402, St Martin d’Hères Cedex, France

    L. Manivel

  2. Dipartimento di Matematica e Informatica, Università di Trieste, Via Valerio 12/1, 34127, Trieste, Italy

    E. Mezzetti

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  1. L. Manivel
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  2. E. Mezzetti
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Correspondence to L. Manivel.

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Manivel, L., Mezzetti, E. On linear spaces of skew-symmetric matrices of constant rank. manuscripta math. 117, 319–331 (2005). https://doi.org/10.1007/s00229-005-0560-7

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  • DOI: https://doi.org/10.1007/s00229-005-0560-7

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