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  3. Polynomials and Vanishing Cycles
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      May 2007
      ISBN:
      9780511543166
      9780521829205
      DOI:
      https://doi.org/10.1017/CBO9780511543166
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.568kg, 266 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology, Algebra
      Series:
      Cambridge Tracts in Mathematics (170)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Tracts in Mathematics (170)
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    Book description

    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.

    Reviews

    '… written in a clear didactic style, with detailed explanations of all notions and results … the book reads fluently, it is accessible for graduate students while advanced researchers … can find here very interesting and useful material …'

    Source: Zentralblatt MATH

    'Each chapter of the book is followed by exercises …'

    Source: EMS Newsletter

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