Hodge Theory and Complex Algebraic Geometry I: Volume 1
Seiten
2007
Cambridge University Press (Verlag)
978-0-521-71801-1 (ISBN)
Cambridge University Press (Verlag)
978-0-521-71801-1 (ISBN)
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 index theorem. Aimed at students, the text is complemented by exercises which provide useful results in complex algebraic geometry.
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.
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.
Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France
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.
| Erscheint lt. Verlag | 20.12.2007 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Übersetzer | Leila Schneps |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 153 x 227 mm |
| Gewicht | 530 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-521-71801-5 / 0521718015 |
| ISBN-13 | 978-0-521-71801-1 / 9780521718011 |
| Zustand | Neuware |
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