Hodge Theory And Complex Algebraic Geometry vol 1

Informationen zum Autor Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France Klappentext The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students. Zusammenfassung 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. Inhaltsverzeichnis 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.

Produktdetails

• Autoren: C. Voisin, Claire Voisin
• Mitarbeit: Bela Bollobas (Herausgeber), Leila Schneps (Übersetzung)
• Verlag: Cambridge University Press Academic
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 15.04.2003
• EAN: 9780521802604
• ISBN: 978-0-521-80260-4
• Abmessung: 157 mm x 234 mm x 20 mm
• Serie: Cambridge Studies in Advanced
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Geometrie