Polynomials and vanishing cycles:
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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
|
| Schriftenreihe: | Cambridge tracts in mathematics
170 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9780511543166 https://doi.org/10.1017/CBO9780511543166 https://doi.org/10.1017/CBO9780511543166 https://doi.org/10.1017/CBO9780511543166 |
| Zusammenfassung: | 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 |
| Umfang: | 1 Online-Ressource (xii, 253 Seiten) |
| ISBN: | 9780511543166 |
| DOI: | 10.1017/CBO9780511543166 |
Internformat
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| 490 | 0 | |a Cambridge tracts in mathematics |v 170 | |
| 505 | 8 | 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 | 4 | |a Algebraic cycles | |
| 650 | 4 | |a Vanishing theorems | |
| 650 | 4 | |a Polynomials | |
| 650 | 4 | |a Hypersurfaces | |
| 650 | 4 | |a Singularities (Mathematics) | |
| 650 | 0 | 7 | |a Polynom |0 (DE-588)4046711-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Verschwindungssatz |0 (DE-588)4187983-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 1 | |a Polynom |0 (DE-588)4046711-9 |D s |
| 689 | 0 | 2 | |a Verschwindungssatz |0 (DE-588)4187983-1 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
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| author | Tibăr, Mihai-Marius 1960- |
| author_GND | (DE-588)133627063 |
| author_facet | Tibăr, Mihai-Marius 1960- |
| author_role | aut |
| author_sort | Tibăr, Mihai-Marius 1960- |
| author_variant | m m t mmt |
| building | Verbundindex |
| bvnumber | BV043942039 |
| classification_rvk | SK 300 |
| collection | ZDB-20-CBO |
| contents | Regularity conditions at infinity Detecting atypical values via singularities at infinity Local and global fibrations Families of complex polynomials Topology of family and contact structures Polar invariants and topology of affine varieties Relative polar curves and families of affine hypersurfaces Monodromy of polynomials Topology of meromorphic functions Slicing by pencils of hypersurfaces Higher Zariski-Lefschetz theorems |
| ctrlnum | (ZDB-20-CBO)CR9780511543166 (OCoLC)850496172 (DE-599)BVBBV043942039 |
| dewey-full | 512.9422 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9422 |
| dewey-search | 512.9422 |
| dewey-sort | 3512.9422 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543166 |
| format | Electronic eBook |
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| id | DE-604.BV043942039 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:18Z |
| institution | BVB |
| isbn | 9780511543166 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351009 |
| oclc_num | 850496172 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xii, 253 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2007 |
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| publisher | Cambridge University Press |
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| spelling | Tibăr, Mihai-Marius 1960- Verfasser (DE-588)133627063 aut Polynomials and vanishing cycles Mihai Tibăr Polynomials & Vanishing Cycles Cambridge Cambridge University Press 2007 1 Online-Ressource (xii, 253 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 170 Preface Regularity conditions at infinity Detecting atypical values via singularities at infinity Local and global fibrations Families of complex polynomials Topology of family and contact structures Polar invariants and topology of affine varieties Relative polar curves and families of affine hypersurfaces Monodromy of polynomials Topology of meromorphic functions Slicing by pencils of hypersurfaces Higher Zariski-Lefschetz theorems 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 Algebraic cycles Vanishing theorems Polynomials Hypersurfaces Singularities (Mathematics) Polynom (DE-588)4046711-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Verschwindungssatz (DE-588)4187983-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Polynom (DE-588)4046711-9 s Verschwindungssatz (DE-588)4187983-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-82920-5 https://doi.org/10.1017/CBO9780511543166 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Tibăr, Mihai-Marius 1960- Polynomials and vanishing cycles Regularity conditions at infinity Detecting atypical values via singularities at infinity Local and global fibrations Families of complex polynomials Topology of family and contact structures Polar invariants and topology of affine varieties Relative polar curves and families of affine hypersurfaces Monodromy of polynomials Topology of meromorphic functions Slicing by pencils of hypersurfaces Higher Zariski-Lefschetz theorems Algebraic cycles Vanishing theorems Polynomials Hypersurfaces Singularities (Mathematics) Polynom (DE-588)4046711-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Verschwindungssatz (DE-588)4187983-1 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4001161-6 (DE-588)4187983-1 |
| title | Polynomials and vanishing cycles |
| title_alt | Polynomials & Vanishing Cycles Regularity conditions at infinity Detecting atypical values via singularities at infinity Local and global fibrations Families of complex polynomials Topology of family and contact structures Polar invariants and topology of affine varieties Relative polar curves and families of affine hypersurfaces Monodromy of polynomials Topology of meromorphic functions Slicing by pencils of hypersurfaces Higher Zariski-Lefschetz theorems |
| title_auth | Polynomials and vanishing cycles |
| title_exact_search | Polynomials and vanishing cycles |
| title_full | Polynomials and vanishing cycles Mihai Tibăr |
| title_fullStr | Polynomials and vanishing cycles Mihai Tibăr |
| title_full_unstemmed | Polynomials and vanishing cycles Mihai Tibăr |
| title_short | Polynomials and vanishing cycles |
| title_sort | polynomials and vanishing cycles |
| topic | Algebraic cycles Vanishing theorems Polynomials Hypersurfaces Singularities (Mathematics) Polynom (DE-588)4046711-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Verschwindungssatz (DE-588)4187983-1 gnd |
| topic_facet | Algebraic cycles Vanishing theorems Polynomials Hypersurfaces Singularities (Mathematics) Polynom Algebraische Geometrie Verschwindungssatz |
| url | https://doi.org/10.1017/CBO9780511543166 |
| work_keys_str_mv | AT tibarmihaimarius polynomialsandvanishingcycles AT tibarmihaimarius polynomialsvanishingcycles |