理想幂次的ai-不变量

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

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.

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.