The residue calculus in several complex variables

Gordon, Gerald Leonard

doi:10.1090/S0002-9947-1975-0430297-3

The residue calculus in several complex variables
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by Gerald Leonard Gordon

Trans. Amer. Math. Soc. 213 (1975), 127-176

DOI: https://doi.org/10.1090/S0002-9947-1975-0430297-3

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Abstract:

Let W be a complex manifold and V an analytic variety. Then homology classes in $W - V$ which bound in V, called the geometric residues, are studied. In fact, a long exact sequence analogous to the Thom-Gysin sequence for nonsingular V is formed by a geometric construction. A geometric interpretation of the Leray spectral sequence of the inclusion of $W - V \subset V$ is also given. If the complex codimension of V is one, then one shows that each cohomology class of $W - V$ can be represented by a differential form of the type $\theta \wedge \lambda + \eta$ where $\lambda$ is the kernel associated to V and $\theta |V$ is the Poincaré residue of this class.

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