摘要翻译:
本文考察了Cohen-Macaulay局部环(R,m)中m-初等理想I的Hilbert系数与相关分次环G(I)的深度之间的关系。这方面的一些结果来自于S.Huckaba和T.Marley的两个定理。这些都是用同调技术证明的。我们用浅表序列给出了简单的证明。
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英文标题:
《Hilbert Coefficients and Depth of the Associated Graded Ring of an Ideal》
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作者:
J. K. Verma
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Commutative Algebra 交换代数
分类描述:Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环,模,理想,同调代数,计算方面,不变理论,与代数几何和组合学的联系
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
In this expository paper we survey results that relate Hilbert coefficients of an m-primary ideal I in a Cohen-Macaulay local ring (R, m) with depth of the associated graded ring G(I). Several results in this area follow from two theorems of S. Huckaba and T. Marley. These were proved using homological techniques. We provide simple proofs using superficial sequences.
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PDF链接:
https://arxiv.org/pdf/0801.4866