Affine semigroups of maximal projective dimension

• Bhardwaj, Om Prakash ^[1] ; Goel, Kriti ^[1] ; Sengupta, Indranath ^[1]
  1. [1] IIT Gandhinagar, Palaj, Gandhinagar, Gujarat, 382355, India
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 3, 2023, págs. 703-727
• Idioma: inglés
• DOI: 10.1007/s13348-022-00370-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • A submonoid of {\mathbb {N}}^d is of maximal projective dimension ({\text {MPD}}) if the associated affine semigroup ring has the maximum possible projective dimension. Such submonoids have a nontrivial set of pseudo-Frobenius elements. We generalize the notion of symmetric semigroups, pseudo-symmetric semigroups, and row-factorization matrices for pseudo-Frobenius elements of numerical semigroups to the case of {\text {MPD}}-semigroups in {\mathbb {N}}^d. Under suitable conditions, we prove that these semigroups satisfy the generalized Wilf’s conjecture. We prove that the generic nature of the defining ideal of the associated semigroup ring of an {\text {MPD}}-semigroup implies uniqueness of row-factorization matrix for each pseudo-Frobenius element. Further, we give a description of pseudo-Frobenius elements and row-factorization matrices of gluing of {\text {MPD}}-semigroups. We prove that the defining ideal of gluing of {\text {MPD}}-semigroups is never generic.

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