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Polynomials and vanishing cycles /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Polynomials and vanishing cycles // Mihai Tibăr.
其他題名:	Polynomials & Vanishing Cycles
作者:	Tibăr, Mihai-Marius,
面頁冊數:	1 online resource (xii, 253 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Singularities (Mathematics) -
電子資源:	https://doi.org/10.1017/CBO9780511543166
ISBN:	9780511543166 (ebook)

Polynomials and vanishing cycles /
Tibăr, Mihai-Marius,1960-

Polynomials and vanishing cycles /Polynomials & Vanishing CyclesMihai Tibăr. - 1 online resource (xii, 253 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;170. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Regularity conditions at infinity --Preface --

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.

ISBN: 9780511543166 (ebook)Subjects--Topical Terms:

527840
Singularities (Mathematics)

LC Class. No.: QA161.P59 / T53 2007

Dewey Class. No.: 512.9422

Polynomials and vanishing cycles /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 2 0 $g Preface -- $t Regularity conditions at infinity -- $t Detecting atypical values via singularities at infinity -- $t Local and global fibrations -- $t Families of complex polynomials -- $t Topology of family and contact structures -- $t Polar invariants and topology of affine varieties -- $t Relative polar curves and families of affine hypersurfaces -- $t Monodromy of polynomials -- $t Topology of meromorphic functions -- $t Slicing by pencils of hypersurfaces -- $t Higher Zariski-Lefschetz theorems.
520 $a 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.
650 0 $a Singularities (Mathematics) $3 527840
650 0 $a Hypersurfaces. $3 785449
650 0 $a Polynomials. $3 528565
650 0 $a Vanishing theorems. $3 1444936
650 0 $a Algebraic cycles. $3 672615
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830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511543166