Singularities and topology of hypersurfaces / Alexandru DimcaType de document : MonographieCollection : UniversitextLangue : anglais.Pays : Etats Unis.Éditeur : New York : Springer, 1992Description : 1 vol. (xvi-263 p.) : ill., appendix ; 24 cmISBN : 9780387977096.ISSN : 0172-5939.Bibliographie : Bibliogr. p. -259. Index.Sujet MSC : 14E15, Algebraic geometry - Birational geometry, Global theory and resolution of singularities
32S30, Several complex variables and analytic spaces - Complex singularities, Deformations of complex singularities; vanishing cycles
14J70, Algebraic geometry - Surfaces and higher-dimensional varieties, Hypersurfaces and algebraic geometry
57R45, Differential topology, Singularities of differentiable mappings
57Q10, Manifolds and cell complexes - PL-topology, Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
14F40, (Co)homology theory in algebraic geometry, de Rham cohomology and algebraic geometryEn-ligne : Springerlink
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Bibliogr. p. -259. Index
The first part consists of three chapters and provides a detailed systematic description of the local topology associated with a hypersurface singularity. The author presents basic tools, methods and many results from the theory of affine hypersurfaces and resolution of singularities, the theory of knots and links, deformation theory and some other areas.
The second part also consists of three chapters. The main goal is to describe an approach to the computation of global topological invariants of complex algebraic hypersurfaces in projective or affine spaces based on knowledge of the local topological information of a singularity. First the author goes into the question of how one can compute the fundamental group of a hypersurface complement in a projective space. (MathSciNet)