Multi-Rees algebras of strongly stable ideals

We prove that the multi-Rees algebra R(I1⊕ ⋯ ⊕ Ir) of a collection of strongly stable ideals I1, … , Ir 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 R(I1⊕ ⋯ ⊕ Ir) based on parameters associated to the collection. Furthermore, we establish a quadratic Gröbner basis of the defining ideal of R(I1⊕ I2) where each of the strongly stable ideals has two quadric Borel generators. As a consequence, we conclude that this multi-Rees algebra is Koszul.

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s13348-022-00385-2

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Work Title Multi-Rees algebras of strongly stable ideals
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Open Access
Creators
  1. Selvi Kara
  2. Kuei Nuan Lin
  3. Gabriel Sosa Castillo
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Collectanea Mathematica
Publication Date November 22, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s13348-022-00385-2
Deposited November 13, 2023

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  • Added Creator Selvi Kara
  • Added Creator Kuei Nuan Lin
  • Added Creator Gabriel Sosa Castillo
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