Mixed Hodge structures:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2008
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete / Folge 3
52 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XIII, 470 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540770152 3540770151 9783642095740 |
Internformat
MARC
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| 100 | 1 | |a Peters, Chris |d 1949- |e Verfasser |0 (DE-588)1036575527 |4 aut | |
| 245 | 1 | 0 | |a Mixed Hodge structures |c Chris A. M. Peters ; Joseph H. M. Steenbrink |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2008 | |
| 264 | 4 | |c © 2008 | |
| 300 | |a XIII, 470 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete / Folge 3 |v 52 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Hodge theory | |
| 650 | 0 | 7 | |a Hodge-Struktur |0 (DE-588)4406134-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hodge-Struktur |0 (DE-588)4406134-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Steenbrink, Joseph H. M. |d 1947- |e Verfasser |0 (DE-588)135540895 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-77017-6 |
| 810 | 2 | |a Folge 3 |t Ergebnisse der Mathematik und ihrer Grenzgebiete |v 52 |w (DE-604)BV000899194 |9 52 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016257231 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 142f 2014 A 2349 |
|---|---|
| DE-BY-TUM_katkey | 1996034 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040080117120 |
| _version_ | 1821933789673160704 |
| adam_text | Contents
Introduction 1
Part I Basic Hodge Theory
1 Compact Kahler Manifolds 11
1.1 Classical Hodge Theory 11
1.1.1 Harmonic Theory 11
1.1.2 The Hodge Decomposition 15
1.1.3 Hodge Structures in Cohomology and Homology 17
1.2 The Lefschetz Decomposition 20
1.2.1 Representation Theory of SL(2, R) 20
1.2.2 Primitive Cohomology 24
1.3 Applications 28
2 Pure Hodge Structures 33
2.1 Hodge Structures 33
2.1.1 Basic Definitions 33
2.1.2 Polarized Hodge Structures 38
2.2 Mumford Tate Groups of Hodge Structures 40
2.3 Hodge Filtration and Hodge Complexes 43
2.3.1 Hodge to De Rham Spectral Sequence 43
2.3.2 Strong Hodge Decompositions 45
2.3.3 Hodge Complexes and Hodge Complexes of Sheaves ... 49
2.4 Refined Fundamental Classes 51
2.5 Almost Kahler V Manifolds 56
3 Abstract Aspects of Mixed Hodge Structures 61
3.1 Introduction to Mixed Hodge Structures: Formal Aspects 62
3.2 Comparison of Filtrations 66
3.3 Mixed Hodge Structures and Mixed Hodge Complexes 69
VIII Contents
3.4 The Mixed Cone 76
3.5 Extensions of Mixed Hodge Structures 79
3.5.1 Mixed Hodge Extensions 79
3.5.2 Iterated Extensions and Absolute Hodge Cohomology . . 83
Part II Mixed Hodge structures on Cohomology Groups
4 Smooth Varieties 89
4.1 Main Result 89
4.2 Residue Maps 92
4.3 Associated Mixed Hodge Complexes of Sheaves 96
4.4 Logarithmic Structures 99
4.5 Independence of the Compactification and Further
Complements 101
4.5.1 Invariance 101
4.5.2 Restrictions for the Hodge Numbers 102
4.5.3 Theorem of the Fixed Part and Applications 103
4.5.4 Application to Lefschetz Pencils 105
5 Singular Varieties 109
5.1 Simplicial and Cubical Sets 109
5.1.1 Basic Definitions 109
5.1.2 Sheaves on Semi simplicial Spaces and Their
Cohomology 114
5.1.3 Cohomological Descent and Resolutions 117
5.2 Construction of Cubical Hyperresolutions 119
5.3 Mixed Hodge Theory for Singular Varieties 124
5.3.1 The Basic Construction 124
5.3.2 Mixed Hodge Theory of Proper Modifications 128
5.3.3 Restriction on the Hodge Numbers 130
5.4 Cup Product and the Kiinneth Formula 133
5.5 Relative Cohomology 135
5.5.1 Construction of the Mixed Hodge Structure 135
5.5.2 Cohomology with Compact Support 137
6 Singular Varieties: Complementary Results 141
6.1 The Leray Filtration 141
6.2 Deleted Neighbourhoods of Algebraic Sets 144
6.2.1 Mixed Hodge Complexes 144
6.2.2 Products and Deleted Neighbourhoods 146
6.2.3 Semi purity of the Link 150
6.3 Cup and Cap Products, and Duality 152
6.3.1 Duality for Cohomology with Compact Supports 152
6.3.2 The Extra Ordinary Cup Product 156
Contents IX
7 Applications to Algebraic Cycles and to Singularities 161
7.1 The Hodge Conjectures 161
7.1.1 Versions for Smooth Projective Varieties 161
7.1.2 The Hodge Conjecture and the Intermediate Jacobian. . 164
7.1.3 A Version for Singular Varieties 166
7.2 Deligne Cohomology 168
7.2.1 Basic Properties 168
7.2.2 Cycle Classes for Deligne Cohomology 172
7.3 The Filtered De Rham Complex And Applications 173
7.3.1 The Filtered De Rham Complex 173
7.3.2 Application to Vanishing Theorems 178
7.3.3 Applications to Du Bois Singularities 183
Part III Mixed Hodge Structures on Homotopy Groups
8 Hodge Theory and Iterated Integrals 191
8.1 Some Basic Results from Homotopy Theory 192
8.2 Formulation of the Main Results 196
8.3 Loop Space Cohomology and the Homotopy De Rham Theoreml99
8.3.1 Iterated Integrals 199
8.3.2 Chen s Version of the De Rham Theorem 201
8.3.3 The Bar Construction 202
8.3.4 Iterated Integrals of 1 Forms 204
8.4 The Homotopy De Rham Theorem for the Fundamental Group205
8.5 Mixed Hodge Structure on the Fundamental Group 208
8.6 The Sullivan Construction 211
8.7 Mixed Hodge Structures on the Higher Homotopy Groups . . . .213
9 Hodge Theory and Minimal Models 219
9.1 Minimal Models of Differential Graded Algebras 220
9.2 Postnikov Towers and Minimal Models; the Simply Connected
Case 222
9.3 Mixed Hodge Structures on the Minimal Model 224
9.4 Formality of Compact Kahler Manifolds 230
9.4.1 The 1 Minimal Model 230
9.4.2 The De Rham Fundamental Group 232
9.4.3 Formality 234
|
| any_adam_object | 1 |
| author | Peters, Chris 1949- Steenbrink, Joseph H. M. 1947- |
| author_GND | (DE-588)1036575527 (DE-588)135540895 |
| author_facet | Peters, Chris 1949- Steenbrink, Joseph H. M. 1947- |
| author_role | aut aut |
| author_sort | Peters, Chris 1949- |
| author_variant | c p cp j h m s jhm jhms |
| building | Verbundindex |
| bvnumber | BV023053902 |
| classification_rvk | SK 240 SK 320 |
| classification_tum | MAT 142f MAT 322f |
| ctrlnum | (OCoLC)244009185 (DE-599)DNB986338613 |
| dewey-full | 516.35 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 514 - Topology |
| dewey-raw | 516.35 514.74 |
| dewey-search | 516.35 514.74 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023053902 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:07:33Z |
| institution | BVB |
| isbn | 9783540770152 3540770151 9783642095740 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016257231 |
| oclc_num | 244009185 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-20 DE-29T DE-703 DE-355 DE-BY-UBR DE-83 DE-11 DE-384 DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-20 DE-29T DE-703 DE-355 DE-BY-UBR DE-83 DE-11 DE-384 DE-91G DE-BY-TUM DE-188 |
| physical | XIII, 470 Seiten Illustrationen, Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / Folge 3 |
| spellingShingle | Peters, Chris 1949- Steenbrink, Joseph H. M. 1947- Mixed Hodge structures Hodge theory Hodge-Struktur (DE-588)4406134-1 gnd |
| subject_GND | (DE-588)4406134-1 |
| title | Mixed Hodge structures |
| title_auth | Mixed Hodge structures |
| title_exact_search | Mixed Hodge structures |
| title_full | Mixed Hodge structures Chris A. M. Peters ; Joseph H. M. Steenbrink |
| title_fullStr | Mixed Hodge structures Chris A. M. Peters ; Joseph H. M. Steenbrink |
| title_full_unstemmed | Mixed Hodge structures Chris A. M. Peters ; Joseph H. M. Steenbrink |
| title_short | Mixed Hodge structures |
| title_sort | mixed hodge structures |
| topic | Hodge theory Hodge-Struktur (DE-588)4406134-1 gnd |
| topic_facet | Hodge theory Hodge-Struktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT peterschris mixedhodgestructures AT steenbrinkjosephhm mixedhodgestructures |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 142f 2014 A 2349 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |