论文标题
强烈稳定理想的多元素代数
Multi-Rees Algebras of Strongly Stable Ideals
论文作者
论文摘要
我们证明了一个强稳定的理想$ i_1，\ ldots，i_r $属于纤维类型的多元素代数$ \ MATHCAL {R}（I_1 \ oplus \ cdots \ oplus i_r）$。特别是，我们为其定义为特殊纤维和二项式Syzygies的Gröbner基础的结合而定为Gröbner提供了一个基础。我们还基于与集合相关的参数研究了$ \ Mathcal {r}（i_1 \ oplus \ cdots \ oplus i_r）$的koszulness。此外，我们建立了$ \ mathcal {r}（i_1 \ oplus i_2）$的定义理想的二次gröbner基础，其中每个强稳定的理想都有两个Quadric Borel发电机。结果，我们得出的结论是，这个多重代数是Koszul。
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.
