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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The residue calculus in several complex variables

Author: Gerald Leonard Gordon
Journal: Trans. Amer. Math. Soc. 213 (1975), 127-176
MSC: Primary 32C30; Secondary 32A25
MathSciNet review: 0430297
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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 \vert V$ is the Poincaré residue of this class.

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Keywords: Residues, analytic varieties, Thom-Gysin sequence, Whitney stratification, tubular neighborhoods, normal crossings, Poincaré residue operator, poles of order one
Article copyright: © Copyright 1975 American Mathematical Society