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Polynomials and vanishing cycles

Author: Mihai-Marius Tibăr
Publisher: Cambridge, UK ; New York : Cambridge University Press, 2007.
Series: Cambridge tracts in mathematics, 170.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"The behavior 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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Mihai-Marius Tibăr
ISBN: 9780521829205 0521829208
OCLC Number: 132289069
Description: xii, 253 pages : illustrations ; 24 cm.
Contents: 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 --
6. Polar invariants and topology of affine varieties --
7. Relative polar curves and families of affine hypersurfaces --
8. Monodromy of polynomials --
9. Topology of meromorphic functions --
10. Slicing by pencils of hypersurfaces --
11. Higher Zariski-Kefschetz theorems --
App. 1. Stratified singularities.
Series Title: Cambridge tracts in mathematics, 170.
Responsibility: Mihai Tibăr.
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Abstract:

A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations; contains the latest research findings.  Read more...

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'... 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 Read more...

 
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   schema:reviewBody ""The behavior 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 especially over the past)5 years, such as holomorphic and mesomorphic 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."--Jacket." ;
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