Year: 2014
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 1 : pp. 34–50
Abstract
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, developed 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, complete intersections or pure-dimensional Cohen-Macaulay spaces. Among other things, several useful applications are considered, which are related with the theory of holonomic $\mathscr{D}$-modules, the theory of Hodge structures, the theory of residual currents and others.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2014.v30.n1.3
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 1 : pp. 34–50
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Logarithmic differential forms de Rham complex regular meromorphic forms holonomic $\mathscr{D}$-modules Poincaré lemma mixed Hodge structure residual currents.