The symmetric geometric rank of symmetric tensors

• Lindberg, Julia ^[1] ; Santarsiero, Pierpaola ^[2]
  1. [1] Georgia Institute of Technology

     Georgia Institute of Technology

     Estados Unidos

     
  2. [2] University of Bologna

     University of Bologna

     Bolonia, Italia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 3, 2026, págs. 791-813
• Idioma: inglés
• DOI: 10.1007/s13348-025-00491-x
• Enlaces
  • Texto completo
• Resumen

  • Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symmetric tensor. This quantity is equal to the codimension of the singular locus of the hypersurface associated to the tensor. We first derive fundamental properties of the symmetric geometric rank. Then, we study the space of symmetric tensors of prescribed symmetric geometric rank, which are spaces of homogeneous polynomials whose corresponding hypersurfaces have a singular locus of bounded codimension.

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