Compact Complex Surfaces

Historical Note.- References.- The Content of the Book.- Standard Notations.- I. Preliminaries.- Topology and Algebra.- Complex Manifolds.- General Analytic Geometry.- Differential Geometry of Complex Manifolds.- Coverings.- Projective-Algebraic Varieties.- II. Curves on Surfaces.- Embedded Curves.- Intersection Theory.- III. Mappings of Surfaces.- Bimeromorphic Geometry.- Fibrations of Surfaces.- The Period Map of Stable Fibrations.- IV. Some General Properties of Surfaces.- 1. Meromorphic Maps Associated to Line Bundles.- 2. Hodge Theory on Surfaces.- 3. Deformations of Surfaces.- 4. Some Inequahties for Hodge Numbers.- 5. Projectivity of Surfaces.- 6. Surfaces of Algebraic Dimension Zero.- 7. Almost-Complex Surfaces without any Complex Structure.- 8. The Vanishing Theorems of Ramanujam and Mumford.- V. Examples.- Some Classical Examples.- Fibre Bundles.- Elliptic Fibrations.- Kodaira Fibrations.- Finite Quotients.- Infinite Quotients.- Double Coverings.- VI. The Enriques-Kodaira Classification.- 1. Statement of the Main Result.- 2. The Castelnuovo Criterion.- 3. The Case a(X) = 2.- 4. The Case a(X) = 1.- 5. The Case a (X) = 0.- 6. The Final Step.- 7. Deformations.- VII. Surfaces of General Type.- Preliminaries.- Two Inequalities.- Pluricanonical Maps.- Surfaces with Given Chern Numbers.- VIII. K3-Surfaces and Enriques Surfaces.- K3-Surfaces.- Enriques Surfaces.- Notations.