Characteristic varieties and vanishing cycles
Characteristic varieties and vanishing cycles
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DOI：
10.1007/bf01388811
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发表时间：
1986-06
影响因子：
3.1
通讯作者：
V. Ginsburg
中科院分区：
文献类型：
--
作者：
V. Ginsburg
0.1.本文系统地研究了具有正则奇点的完整系统的特征簇。这些是余切丛T* X中的圆锥拉格朗日子簇。通过定义，微分算子环~ x上的模的特征簇是T* X上的分次层grJg的支集，它与J//上的良好滤子相关联。设A是它的不可约分支。我们可以把A的类属点处的重数定义为关联的（gr，x层gro//4 '的重数。特征簇的不可约分量的形式线性组合与它们的重数一起计数，称为J/{（cf. [Br2]）。假设J/是完整的（即它的特征变量是拉格朗日的）。则存在一个分层X= IIX~，使得~的特征簇包含在IIT* X [KS ~ 2]中。因此，它的任何不可约分支都是某个余正规丛T* X的闭包。因此，特征周期SS J/r看起来像：
0.1. In this paper we systematically study characteristic varieties of holonomic systems with regular singularities. These are conic Lagrangian subvarieties in the cotangent bundle T* X. By definition, the characteristic variety of a module over the ring~ x of differential operators is the support of the graded sheaf grJg on T* X associated with a good filtration on J//. Let A be its irreducible component. One can define the multiplicity of~'at a generic point of A as a multiplicity of the associated (gr, x-sheaf gro//4'. The formal linear combination of irreducible components of the characteristic variety counted with their multiplicities is called the characteristic cycle of J/{(cf.[Br2]). Suppose J/is holonomic (ie its characteristic variety is Lagrangian). Then there is a stratification X= IIX~ such that the characteristic variety of~ is contained in IIT* X [KS2]. Therefore any its irreducible component is the closure of a certain conormal bundle T* X. Thus the characteristic cycle SS J/r looks like: