A construction of equivariant bundles on the space of symmetric forms

• Ada Boralevi ^[1] ; Daniele Faenzi ^[3] ; Paolo Lella ^[2]
  1. [1] Polytechnic University of Turin

     Polytechnic University of Turin

     Torino, Italia

     
  2. [2] Polytechnic University of Milan

     Polytechnic University of Milan

     Milán, Italia

     
  3. [3] Université de Bourgogne et Franche Comté, Dijon

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 3, 2022, págs. 761-782
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We construct stable vector bundles on the space P(SdCn+1) of symmetric forms of degree d in n+1 variables which are equivariant for the action of SLn+1(C) and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d−1 on Pd, which are moreover equivariant for SL2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.