Atiyah-Chern Character给出了半正则映射和无穷小Abel-Jacobi映射
The Atiyah-Chern Character yields the Semiregularity Map as well as the Infinitesimal Abel-Jacobi Map
摘要：
我们构造了复解析流形或复代数流形上的圈的一般半正则映射，并证明了这种半正则映射可以由经典的Atiyah-Chern特征标工具得到。本文的第一部分是相当详细的，从已知的结果和结构推导出广义半正则映射的存在性和显式形式。我们得到的描述以及无穷小Abel-Jacobi映射的光滑圈作为首项的这个广义半正则映射，说明为什么局部完全相交的适当组成部分，我们的半正则映射与Bloch构造的一致，并给出应用程序嵌入变形和变形的凝聚模。
英文摘要：
We construct a general semiregularity map for cycles on a complex analytic or algebraic manifold and show that such semiregularity map can be obtained from the classical tool of the Atiyah-Chern character. The first part of the paper is fairly detailed, deducing the existence and explicit form of a generalized semiregularity map from known results and constructions. We obtain as well a description of the infinitesimal Abel-Jacobi map for smooth cycles as the leading term of this generalized semiregularity map, indicate why for locally complete intersections the appropriate component of our semiregularity map coincides with the one constructed by Bloch, and give applications to embedded deformations and deformations of coherent modules.
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