The multiplier ideals of a sum of ideals
The multiplier ideals of a sum of ideals
复制标题
理想之和的乘数理想
DOI：
10.1090/s0002-9947-01-02867-7
复制
发表时间：
2001
影响因子：
1.3
通讯作者：
M. Mustaţă
中科院分区：
文献类型：
--
作者：
M. Mustaţă
证明了：若a，B ∈ O X是复光滑簇X上理想的非零层，则对每个γ ∈ Q +，a，B与a + B的乘子理想之间有如下关系：I（X，γ.（a+B））n = I（X，α.a）.I（X，β.B）.α+β=γ两个分次理想系之和的渐近乘子理想也有类似的公式。我们用这个结果来近似在一个给定的点任意乘子理想乘子理想相关联的零维理想。这是适用于比较乘法器的理想相关联的方案在不同的嵌入。
We prove that if a, b ⊂ O X are nonzero sheaves of ideals on a complex smooth variety X, then for every γ ∈ Q + we have the following relation between the multiplier ideals of a, b and a + b: I(X,γ.(a+b)) ⊆ Σ I(X,α.a).I(X,β.b). α+β=γ A similar formula holds for the asymptotic multiplier ideals of the sum of two graded systems of ideals. We use this result to approximate at a given point arbitrary multiplier ideals by multiplier ideals associated to zero dimensional ideals. This is applied to compare the multiplier ideals associated to a scheme in different embeddings.