Collineation varieties of tensors

• Gesmundo, Fulvio ^[1] ; Keneshlou, Hanieh ^[2]
  1. [1] Toulouse Mathematics Institute

     Toulouse Mathematics Institute

     Arrondissement de Toulouse, Francia

     
  2. [2] University of Konstanz

     University of Konstanz

     Landkreis Konstanz, Alemania

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 1, 2026, págs. 257-277
• Idioma: inglés
• DOI: 10.1007/s13348-025-00467-x
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this article, we introduce the k-th collineation variety of a third order tensor. This is the closure of the image of the rational map of size k minors of a matrix of linear forms associated to the tensor. We classify such varieties in the case of pencils of matrices, and nets of matrices of small size. We discuss the natural stratification of tensor spaces induced by the invariants and the geometric type of the collineation varieties.

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