Multi-Rees algebras of strongly stable ideals

• Kara, Selvi ^[1] ; Lin, Kuei-Nuan ^[3] ; Sosa Castillo, Gabriel ^[2]
  1. [1] University of Utah

     University of Utah

     Estados Unidos

     
  2. [2] Colgate University

     Colgate University

     Town of Hamilton, Estados Unidos

     
  3. [3] Department of Mathematics, Penn State University, Greater Allegheny campus 4000 University Dr, McKeesport, PA, 15132, USA

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 213-246
• Idioma: inglés
• DOI: 10.1007/s13348-022-00385-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove that the multi-Rees algebra {\mathcal {R}}(I_1 \oplus \cdots \oplus I_r) of a collection of strongly stable ideals I_1, \ldots , I_r is of fiber type. In particular, we provide a Gröbner basis for its defining ideal as a union of a Gröbner basis for its special fiber and binomial syzygies. We also study the Koszulness of {\mathcal {R}}(I_1 \oplus \cdots \oplus I_r) based on parameters associated to the collection. Furthermore, we establish a quadratic Gröbner basis of the defining ideal of {\mathcal {R}}(I_1 \oplus I_2) where each of the strongly stable ideals has two quadric Borel generators. As a consequence, we conclude that this multi-Rees algebra is Koszul.

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