Our systems are now restored following recent technical disruption, and we’re working hard to catch up on publishing. We apologise for the inconvenience caused. Find out more

Recommended product

Popular links

Popular links


Polynomials and Vanishing Cycles

Polynomials and Vanishing Cycles

Polynomials and Vanishing Cycles

Mihai Tibăr, Université de Lille
May 2007
Hardback
9780521829205
$142.00
USD
Hardback
USD
eBook

    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.

    • Self-contained and accessible tract proposing a systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations
    • The latest research on new topics such as topology of singularities of meromorphic functions and non-generic Lefschetz pencils is discussed in detail
    • Presents the current state of the art in this field

    Reviews & endorsements

    '… 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 …' Zentralblatt MATH

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

    See more reviews

    Product details

    May 2007
    Hardback
    9780521829205
    266 pages
    235 × 160 × 25 mm
    0.568kg
    12 b/w illus. 3 tables 53 exercises
    Available

    Table of Contents

    • Preface
    • Part I. Singularities at Infinity of Polynomial Functions:
    • 1. Regularity conditions at infinity
    • 2. Detecting atypical values via singularities at infinity
    • 3. Local and global fibrations
    • 4. Families of complex polynomials
    • 5. Topology of a family and contact structures
    • Part II. The Impact of Global Polar Varieties:
    • 6. Polar invariants and topology of affine varieties
    • 7. Relative polar curves and families of affine hypersurfaces
    • 8. Monodromy of polynomials
    • Part III. Vanishing Cycles of Non-Generic Pencils:
    • 9. Topology of meromorphic functions
    • 10. Slicing by pencils of hypersurfaces
    • 11. Higher Zariski-Lefschetz theorems
    • Notes
    • References
    • Bibliography
    • Appendix 1. Stratified singularities
    • Appendix 2. Hints to exercises
    • Index.
      Author
    • Mihai Tibăr , Université de Lille

      Mihair Tibar is a Professor in the Mathematics Department at the Université des Sciences et Technologies de Lille, France.