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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Singularities and Topology of Hypersurfaces (Paperback, 1992 ed.)
Loot Price: R2,006
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Singularities and Topology of Hypersurfaces (Paperback, 1992 ed.)
Series: Universitext
Expected to ship within 10 - 15 working days
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From the very beginning, algebraic topology has developed under the
influ- ence of the problems posed by trying to understand the
topological properties of complex algebraic varieties (e.g., the
pioneering work by Poincare and Lefschetz). Especially in the work
of Lefschetz [Lf2], the idea is made explicit that singularities
are important in the study of the topology even in the case of
smooth varieties. What is known nowadays about the topology of
smooth and singular vari- eties is quite impressive. The many
existing results may be roughly divided into two classes as
follows: (i) very general results or theories, like stratified
Morse theory and (mixed) Hodge theory, see, for instance,
Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and
(ii) specific topics of great subtlety and beauty, like the study
of the funda- mental group of the complement in [p>2 of a
singular plane curve initiated by Zariski or Griffiths' theory
relating the rational differential forms to the Hodge filtration on
the middle cohomology group of a smooth projec- tive hypersurface.
The aim of this book is precisely to introduce the reader to some
topics in this latter class. Most of the results to be discussed,
as well as the related notions, are at least two decades old, and
specialists use them intensively and freely in their work.
Nevertheless, it is impossible to find an adequate intro- duction
to this subject, which gives a good feeling for its relations with
other parts of algebraic geometry and topology.
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