The Hodge theory of projective manifolds
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| Format: | Buch |
| Sprache: | English |
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Imperial College Pr.
2007
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| 001 | BV023073523 | ||
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| 005 | 20080318 | ||
| 007 | t | ||
| 008 | 080110s2007 |||| 00||| eng d | ||
| 020 | |a 9781860948008 |9 978-1-86094-800-8 | ||
| 020 | |a 1860948006 |9 1-86094-800-6 | ||
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| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 100 | 1 | |a De Cataldo, Mark Andrea |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Hodge theory of projective manifolds |c Mark Andrea De Cataldo |
| 264 | 1 | |a London |b Imperial College Pr. |c 2007 | |
| 300 | |a X, 102 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Manifolds (Mathematics) |v Congresses | |
| 650 | 0 | 7 | |a Projektive Mannigfaltigkeit |0 (DE-588)4175888-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hodge-Theorie |0 (DE-588)4135967-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Hodge-Theorie |0 (DE-588)4135967-7 |D s |
| 689 | 0 | 1 | |a Projektive Mannigfaltigkeit |0 (DE-588)4175888-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016276645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016276645 | ||
Datensatz im Suchindex
| _version_ | 1804137317918572544 |
|---|---|
| adam_text | Contents
Preface vii
1.
Calculus on smooth manifolds
1
1.1
The Euclidean structure on the exterior algebra
...... 1
1.2
The star isomorphism on
Л(У)
............... 2
1.3
The tangent and cotangent bundles of a smooth manifold
4
1.4
The
de
Rham cohomology groups
..............
б
1.5
Riemannian metrics
..................... 11
1.6
Partitions of unity
...................... 12
1.7
Orientation and integration
................. 12
2.
The Hodge theory of a smooth, oriented, compact
Riemannian manifold
19
2.1
The adjoint of
d
:
d*.....................
19
2.2
The Laplace-Beltrami operator of an oriented Riemannian
manifold
............................ 21
2.3
Harmonic forms and the Hodge Isomorphism Theorem
. . 22
3.
Complex manifolds
27
3.1
Conjugations
......................... 27
3.2
Tangent bundles on a complex manifold
.......... 28
3.3
Cotangent bundles on complex manifolds
......... 31
3.4
The standard orientation of a complex manifold
...... 33
3.5
The quasi complex structure
................ 34
3.6
Complex-valued forms
.................... 37
3.7
Dolbeault and Bott-Chern cohomology
. . ......... 40
4.
Hermitean
linear algebra
43
4.1
The exterior algebra
on
V¿
................. 43
4.2
Bases
............................. 44
4.3
Hermitean metrics
...................... 45
4.4
The inner product and the
*
operator on the complexified
exterior algebra Ac(V^)
................... 48
4.5
The Weil operator
...................... 50
5.
The Hodge theory of Hermitean manifolds
51
5.1
Hermitean metrics on complex manifolds
.......... 51
5.2
The Hodge theory of a compact Hermitean manifold
... 53
6. Kahler
manifolds
57
6.1
The
Kahler
condition
..................... 57
6.2
The fundamental identities of
Kahler
geometry
...... 61
6.3
The Hodge Decomposition for compact
Kahler
manifolds
66
6.4
Some consequences
...................... 69
7.
The Hard Lefschetz Theorem and the Hodge-Riemann
Bilinear Relations
71
7.1
Hodge structures
....................... 72
7.2
The cup product with the Chern class of
a
hyperplane
bundle
74
7.3
The Hard Lefschetz Theorem and the Hodge-Riemann Bi¬
linear Relations
........................ 76
7.4
The Weak Lefschetz Theorem
................ 80
8.
Mixed Hodge structures, semi-simplicity and approximability
83
8.1
The mixed Hodge structure on the cohomology of complex
algebraic varieties
....................... 83
8.2
The Semi-simplicity Theorem
................ 85
8.3
The Leray spectral sequence
.................. 87
8.4
The Global Invariant Cycle Theorem
.............88
8.5
The Lefschetz Theorems and semi-simplicity
........ 89
8.6
Approximability for the space of primitive vectors
.... 93
Bibliography
99
Index
101
|
| adam_txt |
Contents
Preface vii
1.
Calculus on smooth manifolds
1
1.1
The Euclidean structure on the exterior algebra
. 1
1.2
The star isomorphism on
Л(У)
. 2
1.3
The tangent and cotangent bundles of a smooth manifold
4
1.4
The
de
Rham cohomology groups
.
б
1.5
Riemannian metrics
. 11
1.6
Partitions of unity
. 12
1.7
Orientation and integration
. 12
2.
The Hodge theory of a smooth, oriented, compact
Riemannian manifold
19
2.1
The adjoint of
d
:
d*.
19
2.2
The Laplace-Beltrami operator of an oriented Riemannian
manifold
. 21
2.3
Harmonic forms and the Hodge Isomorphism Theorem
. . 22
3.
Complex manifolds
27
3.1
Conjugations
. 27
3.2
Tangent bundles on a complex manifold
. 28
3.3
Cotangent bundles on complex manifolds
. 31
3.4
The standard orientation of a complex manifold
. 33
3.5
The quasi complex structure
. 34
3.6
Complex-valued forms
. 37
3.7
Dolbeault and Bott-Chern cohomology
. . . 40
4.
Hermitean
linear algebra
43
4.1
The exterior algebra
on
V¿
. 43
4.2
Bases
. 44
4.3
Hermitean metrics
. 45
4.4
The inner product and the
*
operator on the complexified
exterior algebra Ac(V^)
. 48
4.5
The Weil operator
. 50
5.
The Hodge theory of Hermitean manifolds
51
5.1
Hermitean metrics on complex manifolds
. 51
5.2
The Hodge theory of a compact Hermitean manifold
. 53
6. Kahler
manifolds
57
6.1
The
Kahler
condition
. 57
6.2
The fundamental identities of
Kahler
geometry
. 61
6.3
The Hodge Decomposition for compact
Kahler
manifolds
66
6.4
Some consequences
. 69
7.
The Hard Lefschetz Theorem and the Hodge-Riemann
Bilinear Relations
71
7.1
Hodge structures
. 72
7.2
The cup product with the Chern class of
a
hyperplane
bundle
74
7.3
The Hard Lefschetz Theorem and the Hodge-Riemann Bi¬
linear Relations
. 76
7.4
The Weak Lefschetz Theorem
. 80
8.
Mixed Hodge structures, semi-simplicity and approximability
83
8.1
The mixed Hodge structure on the cohomology of complex
algebraic varieties
. 83
8.2
The Semi-simplicity Theorem
. 85
8.3
The Leray spectral sequence
. 87
8.4
The Global Invariant Cycle Theorem
.88
8.5
The Lefschetz Theorems and semi-simplicity
. 89
8.6
Approximability for the space of primitive vectors
. 93
Bibliography
99
Index
101 |
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| any_adam_object_boolean | 1 |
| author | De Cataldo, Mark Andrea |
| author_facet | De Cataldo, Mark Andrea |
| author_role | aut |
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| ctrlnum | (OCoLC)154672004 (DE-599)BVBBV023073523 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:34:00Z |
| indexdate | 2024-07-09T21:10:23Z |
| institution | BVB |
| isbn | 9781860948008 1860948006 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016276645 |
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| publisher | Imperial College Pr. |
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| spelling | De Cataldo, Mark Andrea Verfasser aut The Hodge theory of projective manifolds Mark Andrea De Cataldo London Imperial College Pr. 2007 X, 102 S. txt rdacontent n rdamedia nc rdacarrier Manifolds (Mathematics) Congresses Projektive Mannigfaltigkeit (DE-588)4175888-2 gnd rswk-swf Hodge-Theorie (DE-588)4135967-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Hodge-Theorie (DE-588)4135967-7 s Projektive Mannigfaltigkeit (DE-588)4175888-2 s DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016276645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Cataldo, Mark Andrea The Hodge theory of projective manifolds Manifolds (Mathematics) Congresses Projektive Mannigfaltigkeit (DE-588)4175888-2 gnd Hodge-Theorie (DE-588)4135967-7 gnd |
| subject_GND | (DE-588)4175888-2 (DE-588)4135967-7 (DE-588)1071861417 |
| title | The Hodge theory of projective manifolds |
| title_auth | The Hodge theory of projective manifolds |
| title_exact_search | The Hodge theory of projective manifolds |
| title_exact_search_txtP | The Hodge theory of projective manifolds |
| title_full | The Hodge theory of projective manifolds Mark Andrea De Cataldo |
| title_fullStr | The Hodge theory of projective manifolds Mark Andrea De Cataldo |
| title_full_unstemmed | The Hodge theory of projective manifolds Mark Andrea De Cataldo |
| title_short | The Hodge theory of projective manifolds |
| title_sort | the hodge theory of projective manifolds |
| topic | Manifolds (Mathematics) Congresses Projektive Mannigfaltigkeit (DE-588)4175888-2 gnd Hodge-Theorie (DE-588)4135967-7 gnd |
| topic_facet | Manifolds (Mathematics) Congresses Projektive Mannigfaltigkeit Hodge-Theorie Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016276645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT decataldomarkandrea thehodgetheoryofprojectivemanifolds |