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Polynomials and Vanishing Cycles - Mihai Tibăr

Polynomials and Vanishing Cycles

(Autor)

Buch | Hardcover
266 Seiten
2007
Cambridge University Press (Verlag)
978-0-521-82920-5 (ISBN)
CHF 189,95 inkl. MwSt
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.
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.

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

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.

Erscheint lt. Verlag 17.5.2007
Reihe/Serie Cambridge Tracts in Mathematics
Zusatzinfo Worked examples or Exercises; 3 Tables, unspecified; 12 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 160 x 235 mm
Gewicht 568 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-521-82920-8 / 0521829208
ISBN-13 978-0-521-82920-5 / 9780521829205
Zustand Neuware
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