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Polynomials and Vanishing Cycles (Hardcover, New)
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Polynomials and Vanishing Cycles (Hardcover, New)
Series: Cambridge Tracts in Mathematics
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The behaviour of vanishing cycles is the cornerstone for
understanding the geometry and topology of families of
hypersurfaces, usually regarded as singular fibrations. This
self-contained tract proposes a systematic geometro-topological
approach to vanishing cycles, especially those appearing in
non-proper fibrations, such as the fibration defined by a
polynomial function. Topics which have been the object of active
research over the past 15 years, such as holomorphic germs,
polynomial functions, and Lefschetz pencils on quasi-projective
spaces, are here shown in a new light: conceived as aspects of a
single theory with vanishing cycles at its core. Throughout the
book the author presents the current state of the art. Transparent
proofs are provided so that non-specialists can use this book as an
introduction, but all researchers and graduate students working in
differential and algebraic topology, algebraic geometry, and
singularity theory will find this book of great use.
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