000			02838nam a22004098i 4500
001			CR9780511543166
003			UkCbUP
005			20200124160238.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2007||||enk o ||1 0|eng|d
020			_a9780511543166 (ebook)
020			_z9780521829205 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA161.P59 _bT53 2007
082	0	4	_a512.9422 _222
100	1		_aTibăr, Mihai-Marius, _d1960- _eauthor.
245	1	0	_aPolynomials and vanishing cycles / _cMihai Tibăr.
246	3		_aPolynomials & Vanishing Cycles
264		1	_aCambridge : _bCambridge University Press, _c2007.
300			_a1 online resource (xii, 253 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v170
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	2	0	_gPreface -- _tRegularity conditions at infinity -- _tDetecting atypical values via singularities at infinity -- _tLocal and global fibrations -- _tFamilies of complex polynomials -- _tTopology of family and contact structures -- _tPolar invariants and topology of affine varieties -- _tRelative polar curves and families of affine hypersurfaces -- _tMonodromy of polynomials -- _tTopology of meromorphic functions -- _tSlicing by pencils of hypersurfaces -- _tHigher Zariski-Lefschetz theorems.
520			_aThe 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.
650		0	_aAlgebraic cycles.
650		0	_aVanishing theorems.
650		0	_aPolynomials.
650		0	_aHypersurfaces.
650		0	_aSingularities (Mathematics)
776	0	8	_iPrint version: _z9780521829205
830		0	_aCambridge tracts in mathematics ; _v170.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543166
999			_c518226 _d518224