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AuthorBarth, W. author
TitleCompact Complex Surfaces [electronic resource] / by W. Barth, C. Peters, A. Van de Ven
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1984
Connect tohttp://dx.doi.org/10.1007/978-3-642-96754-2
Descript X, 304 p. online resource

SUMMARY

Contents: Introduction. - Standard Notations. - Preliminaries. - Curves on Surfaces. - Mappings of Surfaces. - Some General Properties of Surfaces. - Examples. - The Enriques-Kodaira Classification. - Surfaces of General Type. - K3-Surfaces and Enriques Surfaces. - Bibliography. - Subject Index


CONTENT

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


Mathematics Algebraic geometry Mathematics Algebraic Geometry



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