TY - JOUR
T1 - Multi-Rees algebras of strongly stable ideals
AU - Kara, Selvi
AU - Lin, Kuei Nuan
AU - Castillo, Gabriel Sosa
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Universitat de Barcelona.
PY - 2024/1
Y1 - 2024/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s13348-022-00385-2
DO - 10.1007/s13348-022-00385-2
M3 - Article
AN - SCOPUS:85142444454
SN - 0010-0757
VL - 75
SP - 213
EP - 246
JO - Collectanea Mathematica
JF - Collectanea Mathematica
IS - 1
ER -