Hodge Theory and Complex Algebraic Geometry I: Volume 1

AvClaire Voisin

Häftad, Engelska, 2007

Del 76 i serien Cambridge Studies in Advanced Mathematics

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Beskrivning

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book 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 author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an 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.

Produktinformation

Utgivningsdatum:2007-12-20
Mått:153 x 227 x 18 mm
Vikt:531 g
Format:Häftad
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:334
Förlag:Cambridge University Press
ISBN:9780521718011
Översättare:Leila Schneps

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France

Recensioner i media

'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 steadfastness of purpose, and catching enthusiasm for this fascinating field of contemporary mathematical research. This book is exceedingly instructive, inspiring, challenging and user-friendly, which makes it truly outstanding and extremely valuable for students, teachers, and researchers in complex geometry.' Zentralblatt MATH

Innehållsförteckning

Introduction; Part I. Preliminaries: 1. Holomorphic functions of many variables; 2. Complex manifolds; 3. Kähler metrics; 4. Sheaves and cohomology; Part II. The Hodge Decomposition: 5. Harmonic forms and cohomology; 6. The case of Kähler 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.