### ¹Ö±éÍ×»Ý¡Ê¡¡A.G. Aleksandrov »á¡Ë

The purpose of the talk is to give an elementary introduction to the theory of residue of logarithmic and multi-logarithmic differential forms,
and to describe some of the less known applications of this theory, developed by the author in the past few years.
In particular, we briefly discuss the notion of residue due to H. Poincar'e, J. de Rham, J. Leray and K. Saito, and then obtain an explicit
description of the modules of regular meromorphic differential forms in terms of residues of meromorphic differential forms logarithmic along
hypersurface or complete intersections with arbitrary singularities. We also construct a complex $\Omega_S^\bullet(\log C)$ of sheaves of
multi-logarithmic differential forms on a complex analytic manifold S with respect to a reduced complete intersection $C \subset S,$
and define the residue map as a natural morphism from this complex onto the Barlet complex $\omega_C^\bullet$ of regular meromorphic
differential forms on $C.$ This implies that sections of the Barlet complex can be regarded as a generalization of the residue differential
forms defined by Leray. Summarizing all of these ideas we describe an intrigued generalization of the notion of multi-logarithmic differential
forms to the case of Cohen-Macaulay varieties.

Seminar on Analysis at University of Tsukuba