Residues of Logarithmic Differential Forms in Complex Analysis and Geometry  

作　　者：A.G.Aleksandrov 

机构地区：[1]Institute for Control Sciences,Russian Academy of Sciences, 65 Profsoyunaya str.,B-342, GSP-7, Moscow, 117997, Russian Federation

出　　处：《Analysis in Theory and Applications》2014年第1期34-50,共17页分析理论与应用（英文刊）

摘　　要：In the article, we discuss basic concepts of the residue theory of logarithmic and multi-logarithmic differential forms, and describe some aspects of the theory, de-veloped by the author in the past few years. In particular, we introduce the notion of logarithmic differential forms with the use of the classical de Rham lemma and give an explicit description of regular meromorphic differential forms in terms of residues of logarithmic or multi-logarithmic differential forms with respect to hypersurfaces, com-plete intersections or pure-dimensional Cohen-Macaulay spaces. Among other things, several useful applications are considered, which are related with the theory of holo-nomic D-modules, the theory of Hodge structures, the theory of residual currents and others.In the article, we discuss basic concepts of the residue theory of logarithmic and multi-logarithmic differential forms, and describe some aspects of the theory, de-veloped by the author in the past few years. In particular, we introduce the notion of logarithmic differential forms with the use of the classical de Rham lemma and give an explicit description of regular meromorphic differential forms in terms of residues of logarithmic or multi-logarithmic differential forms with respect to hypersurfaces, com-plete intersections or pure-dimensional Cohen-Macaulay spaces. Among other things, several useful applications are considered, which are related with the theory of holo-nomic D-modules, the theory of Hodge structures, the theory of residual currents and others.

关 键 词：Logarithmic differential forms de Rham complex regular meromorphic forms holo-nomic D-modules Poincare lemma mixed Hodge structure residual currents. 

分 类 号：O174.52[理学—数学]