
Polynomials and Vanishing Cycles
Mihai Tibar(Author)
Cambridge University Press
Published on 17. May 2007
Book
Hardback
266 pages
978-0-521-82920-5 (ISBN)
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 / Votes
'... 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 NewsletterMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 3 Tables, unspecified; 12 Line drawings, unspecified
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 20 mm
Weight
587 gr
ISBN-13
978-0-521-82920-5 (9780521829205)
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Schweitzer Classification
Other editions
Additional editions

Mihai Tibar
Polynomials and Vanishing Cycles
E-Book
06/2007
1st Edition
Cambridge University Press
€70.99
Available for download
Person
Mihair Tibar is a Professor in the Mathematics Department at the Universite des Sciences et Technologies de Lille, France.
Content
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.