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On Leray’s residue theory. (English. Russian original) Zbl 0731.32002
Global Analysis - studies and applications IV, Lect. Notes Math. 1453, 109-119 (1990); translation from Global’nyj Analiz i Nelinejnye Uravneniya, Nov. Global’nom Anal. 1988, 159-167 (1988).
[For the entire collection see Zbl 0708.00012.]
In Leray’s theory, the residue form of a form with singularities of high order is defined by first passing to a cohomologous form with first-order singularities that is not, in general, constructively defined. See, for example, § 16 of the book of L. A. Ajzenberg and A. P. Yuzhakov [Integral representations and residues in multidimensional complex analysis (Russian) (1979; Zbl 0445.32002); English translation in (1983; Zbl 0537.32002)]. The authors propose a direct definition of the residue of a cohomology class based on integration along the fibers of the normal bundle to the set of singularities.
MSC:
32A27 Residues for several complex variables
32C30 Integration on analytic sets and spaces, currents