理想幂次的ai-不变量

doi:10.3969/j.issn.0253-2778.2020.03.013

中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (3): 349-359.DOI: 10.3969/j.issn.0253-2778.2020.03.013

理想幂次的ai-不变量

田世新，申伊塃

1.中国科学技术大学数学科学学院, 安徽合肥 230026; 2.中国科学院吴文俊数学重点实验室(中国科学技术大学), 安徽合肥 230026

收稿日期:2020-01-06 修回日期:2020-03-28 接受日期:2020-03-28 出版日期:2020-03-31 发布日期:2020-03-28

The ai-invariants of powers of ideals

TIAN Shixin, SHEN Yihuang,2

Received:2020-01-06 Revised:2020-03-28 Accepted:2020-03-28 Online:2020-03-31 Published:2020-03-28
Contact: SHEN Yihuang
About author:TIAN Shixin, male, born in 1995, Master. Research field: Algebra. E-mail: tsx@mail.ustc.edu.cn
Supported by:
Supported by the Fundamental Research Funds for the Central Universities(AHY150200).

摘要/Abstract

摘要： 在Lu和O’Rourke最近的工作基础上, 我们研究了分次理想及其幂次的ai-不变量. 设R和S是域K上的两个多项式环, T=SK R, I和J分别是R和S中的分次理想. 我们利用I和J的信息研究ai(T/(I+J+mn)k)的性质. 再设k≥2, 并令Δ为一个k维复形且IΔ是其Stanley-Reisner理想. 我们研究I(n)Δ的ai-不变量.

关键词: ai-不变量, 局部上同调, 复形, 形式幂

Abstract: Inspired by the recent work of Lu and O’Rourke, we study the ai-invariants of (symbolic) powers of some graded ideals. When I and J are two graded ideals in two distinct polynomial rings R and S over a common field K. We study the ai-invariants of the powers of the fiber product via the corresponding conditions on I and J. When IΔ is the Stanley-Reisner ideal of a k-dimensional complex Δ with k≥2. We investigate the ai-invariants of the symbolic powers of IΔ.

Key words: ai-invariants, local cohomology, complex, symbolic power

中图分类号:

O153.3

田世新，申伊塃. 理想幂次的ai-不变量[J]. 中国科学技术大学学报, 2020, 50(3): 349-359.

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理想幂次的ai-不变量

The ai-invariants of powers of ideals

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