The F-singularities of algebras defined by permanents

• Chau, Trung ^[1]
  1. [1] Chennai Mathematical Institute

     Chennai Mathematical Institute

     India

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 3, 2026, págs. 843-859
• Idioma: inglés
• DOI: 10.1007/s13348-025-00494-8
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let X be a matrix of indeterminates, t an integer, and P_t(X) define the ideal generated by the permanents of all t\times t submatrix of X. P_t(X) is called a permanental ideal. In this article, we study the algebras \Bbbk [X]/P_t(X) where X is a generic, symmetric, or a Hankel matrix of indeterminates. When {{\,\textrm{char}\,}}\Bbbk = 2, P_t(X) is also known as a determinantal ideal, a popular class in commutative algebra and algebraic geometry, and thus many properties of P_t(X) are known in this case. We prove that, if X is an n\times n matrix and {{\,\textrm{char}\,}}\Bbbk >2, the algebra \Bbbk [X]/P_n(X) is F-regular, just like when {{\,\textrm{char}\,}}\Bbbk = 2. On the other hand, we obtain a full characterization of when \Bbbk [X]/P_2(X) is F-pure or F-regular, when {{\,\textrm{char}\,}}\Bbbk >2, and the answer is different than that in even characteristic.

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