Némethi, András Lefschetz theory for complex affine varieties. (English) Zbl 0665.14003 Rev. Roum. Math. Pures Appl. 33, No. 3, 233-250 (1988). 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 Cited in 11 Documents MSC: 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 14F45 Topological properties in algebraic geometry Keywords:Lefschetz theory on complex affine varieties; hyperplane sections Citations:Zbl 0526.14010 PDFBibTeX XMLCite \textit{A. Némethi}, Rev. Roum. Math. Pures Appl. 33, No. 3, 233--250 (1988; Zbl 0665.14003)