当前位置: X-MOL 学术Invent. math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Square-free Gröbner degenerations
Inventiones mathematicae ( IF 2.6 ) Pub Date : 2020-03-06 , DOI: 10.1007/s00222-020-00958-7
Aldo Conca , Matteo Varbaro

Let I be a homogeneous ideal of $$S=K[x_1,\ldots , x_n]$$ and let J be an initial ideal of I with respect to a term order. We prove that if J is radical then the Hilbert functions of the local cohomology modules supported at the homogeneous maximal ideal of S/I and S/J coincide. In particular, $${\text {depth}} (S/I)={\text {depth}} (S/J)$$ and $${\text {reg}} (S/I)={\text {reg}} (S/J)$$.

中文翻译:

无平方 Gröbner 退化

令 I 为 $$S=K[x_1,\ldots , x_n]$$ 的齐次理想,并令 J 为 I 关于项阶的初始理想。我们证明,如果 J 是激进的,那么 S/I 和 S/J 的齐次极大理想所支持的局部上同调模的希尔伯特函数重合。特别地,$${\text {depth}} (S/I)={\text {depth}} (S/J)$$ 和 $${\text {reg}} (S/I)={\文本 {reg}} (S/J)$$。
更新日期:2020-03-06
down
wechat
bug