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Cambridge Tracts in Mathematics #170: Polynomials and Vanishing Cycles

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Cambridge Tracts in Mathematics #170: Polynomials and Vanishing Cycles Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations is proposed in this tract. Lefschetz theory, complex Morse theory and singularities of hypersurfaces are presented in detail leading to the latest research on topics such as the topology of singularities of meromorphic functions and non-generic Lefschetz pencils.

About the Author

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

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.

Product Details

ISBN:
9780521829205
Author:
Tibar, Mihai
Publisher:
Cambridge University Press
Author:
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Author:
Tib&#259 R., Mihai
Author:
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Author:
Mihai, Tib&#259 R.
Author:
259
Author:
R
Author:
Tib
Author:
Mihai Tib
Location:
Cambridge
Subject:
Applied
Subject:
Singularities (mathematics)
Subject:
Polynomials
Subject:
Mathematics-Applied
Copyright:
Edition Description:
Hardcover
Series:
Cambridge Tracts in Mathematics
Series Volume:
170
Publication Date:
20070531
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
12 line diagrams 3 tables 53 exercis
Pages:
266

Related Subjects


Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry

Cambridge Tracts in Mathematics #170: Polynomials and Vanishing Cycles Sale Hardcover
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Product details 266 pages Cambridge University Press - English 9780521829205 Reviews:
"Synopsis" by , A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations is proposed in this tract. Lefschetz theory, complex Morse theory and singularities of hypersurfaces are presented in detail leading to the latest research on topics such as the topology of singularities of meromorphic functions and non-generic Lefschetz pencils.
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