zbMATH — the first resource for mathematics

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.
32A27 Residues for several complex variables
32C30 Integration on analytic sets and spaces, currents