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Vanishing cycles of pencils of hypersurfaces
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In this paper, an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, was proposed and the module of vanishing cycles was generated by the images of certain variation maps.Abstract:
We prove an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, and show that the module of vanishing cycles is generated by the images of certain variation maps.read more
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MonographDOI
The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils
TL;DR: In this article, a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces was proved.
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Zariski-van Kampen theorem for higher homotopy groups
D. Chéniot,Anatoly Libgober +1 more
TL;DR: In this paper, the fundamental groups of the complements of plane singular curves by generators and relations are described by an extension of the classical Zariski-van Kampen theorem.
Journal ArticleDOI
Density of monodromy actions on non-abelian cohomology
TL;DR: In this article, the monodromy action on the first Betti and de Rham non-Abelian cohomology arising from a family of smooth curves was studied.
Book
Complex analytic singularities
立雄 諏訪,Philip Wagreich +1 more
TL;DR: In this article, Abhyankar et al. present a collection of papers by S.S.-T. Yau and A.B.Bialynicki-Birula, W. Casselman, A.H. Hauser, M.-N. Ishida, S.Iwashita, M.N. Nakamura, I.Saito, N. Sasakura, L.S. Tomari, H.Tsuchihashi, K.Tomari, T.N Nagase, I Nakamura and I.Naruki
Posted Content
On higher homotopy groups of pencils
TL;DR: In this paper, the second Lefschetz theorem for higher homotopy groups was proved for a class of pencils on singular complex spaces, which is known as the so-called second lefschetz theorem.
References
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Book
Singular points of complex hypersurfaces
TL;DR: The Singular Points of Complex Hypersurfaces (AM-61) as mentioned in this paper is a seminal work in the area of complex hypersurfaces, and is based on as mentioned in this paper.
Book
Stratified Morse theory
Mark Goresky,Robert MacPherson +1 more
TL;DR: In this paper, the fundamental problem of Morse theory is to study the topological changes in the space X ≤c as the number c varies, where X is a topological space and c is a real number.
Journal Article
Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux
TL;DR: Laszlo as mentioned in this paper proved Lefschetz's theorem for both the fundamental group and the Picard group for both groups, and proved the same theorem for the Picard groups as well.
Book
Isolated Singular Points on Complete Intersections
TL;DR: In this paper, the authors give a coherent account of the theory of isolated singularities of complete intersections, and show that the discriminant of the semi-universal deformation of an A-D-E singularity is isomorphic to the associated Coxeter group.
Journal ArticleDOI
Ensembles et morphismes stratifiés
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