Rees Algebras of Modules
Rees Algebras of Modules
复制标题
模的里斯代数
DOI：
10.1112/s0024611502014144
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发表时间：
2003
影响因子：
1.8
通讯作者：
W. Vasconcelos
中科院分区：
文献类型：
--
作者：
A. Simis;B. Ulrich;W. Vasconcelos
我们在一个相当一般的框架内研究Rees代数的模。我们介绍了一种方法，通过布尔巴基理想的概念，允许使用变形理论。我们可以讨论模E的（本质上唯一的）一般布尔巴基理想I（E），在许多情况下，它允许我们将E的里斯代数的性质还原为其布尔巴基理想I（E）的性质。从这个角度来看，如科恩-麦考莱，正常性和线性类型的属性。在模的情况下，考虑了理想及其相关代数的已知数值不变量，如解析展度、约化数和解析偏差。相应的概念完全交，几乎完全交和equimultiple模进行了一些详细的检查。特别考虑到某些模块是相当普遍的，因为有趣的向量丛出现在这种方式。对于这些模，人们能够根据Buchsbaum-Rim重数估计约简数和其他不变量。2000年数学科目分类13 A30（小学）、13 H10、13 B21（中学）
We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allows the use of deformation theory. One can talk about the (essentially unique) generic Bourbaki ideal I(E) of a module E which, in many situations, allows one to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Macaulayness, normality and being of linear type are viewed from this perspective. The known numerical invariants, such as the analytic spread, the reduction number and the analytic deviation, of an ideal and its associated algebras are considered in the case of modules. Corresponding notions of complete intersection, almost complete intersection and equimultiple modules are examined in some detail. Special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way. For these modules one is able to estimate the reduction number and other invariants in terms of the Buchsbaum–Rim multiplicity. 2000 Mathematics Subject Classification 13A30 (primary), 13H10, 13B21 (secondary)