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Lefschetz theory for complex affine varieties. (English) Zbl 0665.14003
The author works out a Lefschetz theory on complex affine varieties. His approach is to construct and integrate explicit vector fields to get the local triviality of some mappings. - In particular, he gets the affine versions of the theorems about the locally trivial bundle structure and the Lefschetz-vanishing-theorems of hyperplane sections.
The results contain as a special case the work of S. A. Broughton [in Singularities, Summer Inst., Arcata/Calif. 1981, Proc. Symp. Pure Math. 40, Part 1, 167-178 (1983; Zbl 0526.14010)] on polynomial mappings.
Reviewer: K.Drechsler

14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14F45 Topological properties in algebraic geometry