Multiplicity of functions on singular varieties
Multiplicity of functions on singular varieties
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单一品种上的多重函数
DOI：
10.1142/s0129167x03001910
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Suwa
中科院分区：
文献类型：
--
作者：
Takeshi Izawa;T. Suwa
设V是复流形W中的局部完全交。对于W上的函数g，我们设f = g| V和f′ = g| V '，其中V'表示V的非奇异部分。对于V的奇异集和f '的临界集的并的每个紧连通分量S，我们将f在S处的虚重数定义为V的虚余切丛的Chern类的df'定位的留数。f在S处的重数m（f，S）则定义为，其中μ（V，[2]的（广义）Milnor数。当S = {p}是孤立点且g是全纯的时，我们给出了B作为V上的Grothendieck剩余的一个显式表达式.在V到Riemann曲面上的全纯映射的整体情形下，我们证明了B的一个公式的奇异形式. Iversen [13].
Let V be a local complete intersection in a complex manifold W. For a function g on W, we set f = g|V and f′ = g|V′, where V′ denotes the non-singular part of V. For each compact connected component S of the union of the singular set of V and the critical set of f′, we define the virtual multiplicity of f at S as the residue of the localization by df′ of the Chern class of the virtual cotangent bundle of V. The multiplicity m(f, S) of f at S is then defined by , where μ(V, S) is the (generalized) Milnor number of [2]. If S = {p} is an isolated point and if g is holomorphic, we give an explicit expression of as a Grothendieck residue on V. In the global situation, where we have a holomorphic map of V onto a Riemann surface, we prove a singular version of a formule of B. Iversen [13].