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Hodge theory and complex algebraic geometry

Author: Claire Voisin
Publisher: Cambridge ; New York : Cambridge University Press, ©2002-2003.
Series: Cambridge studies in advanced mathematics, 76-77.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This is a modern introduction to Kaehlerian geometry and Hodge structure. It starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Claire Voisin
ISBN: 0521802601 9780521802604 0521802830 9780521802833
OCLC Number: 48803407
Description: 2 volumes ; 24 cm.
Contents: Introduction; Part I. Preliminaries: 1. Holomorphic functions of many variables; 2. Complex manifolds; 3. Kahler metrics; 4. Sheaves and cohomology; Part II. The Hodge Decomposition: 5. Harmonic forms and cohomology; 6. The case of Kahler manifolds; 7. Hodge structures and polarisations; 8. Holomorphic de Rham complexes and spectral sequences; Part III. Variations of Hodge Structure: 9. Families and deformations; 10. Variations of Hodge structure; Part IV. Cycles and Cycle Classes: 11. Hodge classes; 12. Deligne-Beilinson cohomology and the Abel-Jacobi map; Bibliography; Index.
Series Title: Cambridge studies in advanced mathematics, 76-77.
Other Titles: Théorie de Hodge et géométrie algébrique complexe.
Responsibility: Claire Voisin ; translated by Leila Schneps.
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This is a completely self-contained modern introduction to Kaehlerian geometry and Hodge structure. The author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge  Read more...

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'This introductory text to Hodge theory and Kahlerian geometry is an excellent and modern introduction to the subject, shining with comprehensiveness, strictness, clarity, rigor, thematic Read more...

 
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Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/48803407<\/a>> # Hodge theory and complex algebraic geometry<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:CreativeWork<\/a>, schema:Book<\/a> ;\u00A0\u00A0\u00A0\nbgn:translationOfWork<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/48803407#CreativeWork\/unidentifiedOriginalWork<\/a>> ; # Th\u00E9orie de Hodge et g\u00E9om\u00E9trie alg\u00E9brique complexe.<\/span>\n\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"48803407<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Place\/cambridge<\/a>> ; # Cambridge<\/span>\n\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> ; # New York<\/span>\n\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/enk<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/hodge_theorie<\/a>> ; # Hodge-Theorie<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/geometry_algebraic<\/a>> ; # Geometry, Algebraic<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/31_42_functions_of_one_complex_variable<\/a>> ; # 31.42 functions of one complex variable<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/hodge_theorie_de<\/a>> ; # Hodge, Th\u00E9orie de<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/algebraische_meetkunde<\/a>> ; # Algebra\u00EFsche meetkunde<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/516.35\/e21\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/geometrie_algebrique<\/a>> ; # G\u00E9om\u00E9trie alg\u00E9brique<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/hodge_theory<\/a>> ; # Hodge theory<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/31_51_algebraic_geometry<\/a>> ; # 31.51 algebraic geometry<\/span>\n\u00A0\u00A0\u00A0\nschema:bookFormat<\/a> bgn:PrintBook<\/a> ;\u00A0\u00A0\u00A0\nschema:copyrightYear<\/a> \"2002\/2003<\/span>\" ;\u00A0\u00A0\u00A0\nschema:creator<\/a> <http:\/\/viaf.org\/viaf\/59148417<\/a>> ; # Claire Voisin<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2002\/2003<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This is a modern introduction to Kaehlerian geometry and Hodge structure. It starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions. The book is is completely self-contained and can be used by students, while its content gives an up-to-date account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/709956<\/a>> ; # Th\u00E9orie de Hodge et g\u00E9om\u00E9trie alg\u00E9brique complexe.<\/span>\n\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Series\/cambridge_studies_in_advanced_mathematics<\/a>> ; # Cambridge studies in advanced mathematics ;<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Hodge theory and complex algebraic geometry<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"48803407<\/span>\" ;\u00A0\u00A0\u00A0\nschema:publication<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/48803407#PublicationEvent\/cambridge_new_york_cambridge_university_press_2002_2003<\/a>> ;\u00A0\u00A0\u00A0\nschema:publisher<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Agent\/cambridge_university_press<\/a>> ; # Cambridge University Press<\/span>\n\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/catdir.loc.gov\/catdir\/samples\/cam033\/2002017389.html<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.myilibrary.com?id=41829<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/catdir.loc.gov\/catdir\/toc\/cam027\/2002017389.html<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/site.ebrary.com\/id\/10069838<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.myilibrary.com?id=41831<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780521802604<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780521802833<\/a>> ;\u00A0\u00A0\u00A0\numbel:isLike<\/a> <http:\/\/bnb.data.bl.uk\/id\/resource\/GBA303176<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/48803407<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Related Entities<\/h3>\n
<http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> # New York<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"New York<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/dewey.info\/class\/516.35\/e21\/<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Agent\/cambridge_university_press<\/a>> # Cambridge University Press<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:Agent<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Cambridge University Press<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Place\/cambridge<\/a>> # Cambridge<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Cambridge<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Series\/cambridge_studies_in_advanced_mathematics<\/a>> # Cambridge studies in advanced mathematics ;<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:PublicationSeries<\/a> ;\u00A0\u00A0\u00A0\nschema:hasPart<\/a> <http:\/\/www.worldcat.org\/oclc\/48803407<\/a>> ; # Hodge theory and complex algebraic geometry<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Cambridge studies in advanced mathematics ;<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/31_42_functions_of_one_complex_variable<\/a>> # 31.42 functions of one complex variable<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"31.42 functions of one complex variable<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/31_51_algebraic_geometry<\/a>> # 31.51 algebraic geometry<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"31.51 algebraic geometry<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/algebraische_meetkunde<\/a>> # Algebra\u00EFsche meetkunde<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Algebra\u00EFsche meetkunde<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/geometrie_algebrique<\/a>> # G\u00E9om\u00E9trie alg\u00E9brique<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"G\u00E9om\u00E9trie alg\u00E9brique<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"G\u00E9om\u00E9trie alg\u00E9brique<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/geometry_algebraic<\/a>> # Geometry, Algebraic<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Geometry, Algebraic<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/hodge_theorie<\/a>> # Hodge-Theorie<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Hodge-Theorie<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/hodge_theorie_de<\/a>> # Hodge, Th\u00E9orie de<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Hodge, Th\u00E9orie de<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Hodge, Th\u00E9orie de<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/709956#Topic\/hodge_theory<\/a>> # Hodge theory<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Hodge theory<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/enk<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"enk<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/59148417<\/a>> # Claire Voisin<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1962<\/span>\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Voisin<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Claire<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Claire Voisin<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/entity\/work\/id\/709956<\/a>> # Th\u00E9orie de Hodge et g\u00E9om\u00E9trie alg\u00E9brique complexe.<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Th\u00E9orie de Hodge et g\u00E9om\u00E9trie alg\u00E9brique complexe.<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/worldcat.org\/isbn\/9780521802833<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"0521802830<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9780521802833<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/48803407<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/48803407<\/a>> ; # Hodge theory and complex algebraic geometry<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2020-12-06<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/48803407#CreativeWork\/unidentifiedOriginalWork<\/a>> # Th\u00E9orie de Hodge et g\u00E9om\u00E9trie alg\u00E9brique complexe.<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"fr<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Th\u00E9orie de Hodge et g\u00E9om\u00E9trie alg\u00E9brique complexe.<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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Content-negotiable representations<\/p>\n