Compact Complex Surfaces [Paperback]

Contents: Introduction. - Standard Notations. -Preliminaries. - Curves on Surfaces. - Mappings of Surfaces.- Some General Properties of Surfaces. - Examples. - TheEnriques-Kodaira Classification. - Surfaces of General Type.- K3-Surfaces and Enriques Surfaces. - Bibliography. -Subject Index.Contents: Introduction. - Standard Notations. -Preliminaries. - Curves on Surfaces. - Mappings of Surfaces.- Some General Properties of Surfaces. - Examples. - TheEnriques-Kodaira Classification. - Surfaces of General Type.- K3-Surfaces and Enriques Surfaces. - Bibliography. -Subject Index.Historical Note.- References.- The Content of the Book.- Standard Notations.- I. Preliminaries.- Topology and Algebra.- 1. Notations and Basic Facts.- 2. Some Properties of Bilinear forms.- 3. Vector Bundles, Characteristic Classes and the Index Theorem.- Complex Manifolds.- 4. Basic Concepts and Facts.- 5. Holomorphic Vector Bundles, Serre Duality and the Riemann-Roch Theorem.- 6. Line Bundles and Divisors.- 7. Algebraic Dimension and Kodaira Dimension.- General Analytic Geometry.- 8. Complex Spaces.- 9. The ?-Process.- 10. Deformations of Complex Manifolds.- Differential Geometry of Complex Manifolds.- 11. De Rham Cohomology.- 12. Dolbeault Cohomology.- 13. K?hler Manifolds.- 14. Weight-1 Hodge Structures.- 15. Yaus Results on K?hler-Einstein Metrics.- Coverings.- 16. Ramification.- 17. Cyclic Coverings.- 18. Covering Tricks.- Projective-Algebraic Varieties.- 19. GAGA Theorems and Projectivity Criteria.- 20. Theorems of Bertini and Lefschetz.- II. Curves on Surfaces.- Embedded Curves.- 1. Some Standard Exact Sequences.- 2. The Picard-Group of an Embedded Curve.- 3. Riemann-Roch for an Embedded Curve.- 4. The Residue Theorem.- 5. The Trace Map.- 6. Serre Duality on an Embedded Curve.- 7. The ?-Process.- 8. Simple Singularities of Curves.- Intersection Theory.- 9. Intersection Multiplicities.- 10. Intersection Numbers.- 11. The Arithmetical Genus of an Embedded Curve.- 12. 1l³