Chéniot, Denis Vanishing cycles in a pencil of hyperplane sections of a non-singular quasi-projective variety. (English) Zbl 0851.14003 Proc. Lond. Math. Soc., III. Ser. 72, No. 3, 515-544 (1996). We give an inductive way to obtain the vanishing cycles which occur in the “second Lefschetz theorem” about pencils of hyperplane sections of a non-singular projective variety. In fact we do this for the more general case of a non-singular quasi-projective variety. As a corollary, we show that the Lefschetz hyperplane section theorem for a non-singular quasi-projective variety can be made more precise in the middle dimension by a statement which recalls the theorem of von Kampen on the fundamental group of the complement of a plane projective curve. Reviewer: D.Chéniot (Marseille) Cited in 1 ReviewCited in 4 Documents MSC: 14C25 Algebraic cycles 14C21 Pencils, nets, webs in algebraic geometry 14J70 Hypersurfaces and algebraic geometry Keywords:second Lefschetz theorem; vanishing cycles; pencils of hyperplane sections; fundamental group of the complement of a plane projective curve PDFBibTeX XMLCite \textit{D. Chéniot}, Proc. Lond. Math. Soc. (3) 72, No. 3, 515--544 (1996; Zbl 0851.14003) Full Text: DOI