2020/12/31 by Selvi Kara, Kara, Selvi, Kuei-Nuan Lin +3
Mathematics · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2012.15447
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.