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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License | In Copyright (Rights Reserved) |
Work Type | Article |
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Publication Date | November 22, 2022 |
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Deposited | November 13, 2023 |
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