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• catalog abstract "The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.".
• catalog contributor b9539284.
• catalog created "1996.".
• catalog date "1996".
• catalog date "1996.".
• catalog dateCopyrighted "1996.".
• catalog description "1. Vector bundles over complex manifolds. 1.1. Vector bundles. 1.2. Chern classes. 1.3. GAGA Theorems. 1.4. Torsion-free and reflexive coherent sheaves. 1.5. Problems on vector bundles -- 2. Facts on compact complex surfaces. 2.1. Line bundles and divisors. 2.2. Algebraic dimension and Kodaira dimension. 2.3. Classification and examples of surfaces. 2.4. Intersection form and Neron-Severi group -- 3. Line bundles over surfaces. 3.1. Holomorphic structures in line bundles. 3.2. Picard group for tori. 3.3. Neron-Severi group for some elliptic surfaces. 3.4. Picard group for primary Kodaira surfaces -- 4. Existence of holomorphic vector bundles. 4.1. Serre construction. 4.2. Filtrable vector bundles. 4.3. Non-filtrable and irreducible vector bundles. 4.4. Simple filtrable vector bundles -- 5. Classification of vector bundles. 5.1. Deformations of vector bundles and applications. 5.2. Moduli spaces of simple vector bundles. 5.3. Stable vector bundles.".
• catalog description "Includes bibliographical references (p.[157]-165) and index.".
• catalog description "The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.".
• catalog extent "viii, 170 p. ;".
• catalog hasFormat "Holomorphic vector bundles over compact complex surfaces.".
• catalog identifier "3540610189 (softcover : alk. paper)".
• catalog isFormatOf "Holomorphic vector bundles over compact complex surfaces.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1624.".
• catalog isPartOf "Lecture notes in mathematics ; 1624".
• catalog issued "1996".
• catalog issued "1996.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog relation "Holomorphic vector bundles over compact complex surfaces.".
• catalog subject "510 s 514/.224 20".
• catalog subject "Algebraic topology.".
• catalog subject "Complex manifolds.".
• catalog subject "Geometry, algebraic.".
• catalog subject "Global differential geometry.".
• catalog subject "Mathematics.".
• catalog subject "QA3 .L28 no. 1624 QA612.63".
• catalog subject "Surfaces, Algebraic.".
• catalog subject "Vector bundles.".
• catalog tableOfContents "1. Vector bundles over complex manifolds. 1.1. Vector bundles. 1.2. Chern classes. 1.3. GAGA Theorems. 1.4. Torsion-free and reflexive coherent sheaves. 1.5. Problems on vector bundles -- 2. Facts on compact complex surfaces. 2.1. Line bundles and divisors. 2.2. Algebraic dimension and Kodaira dimension. 2.3. Classification and examples of surfaces. 2.4. Intersection form and Neron-Severi group -- 3. Line bundles over surfaces. 3.1. Holomorphic structures in line bundles. 3.2. Picard group for tori. 3.3. Neron-Severi group for some elliptic surfaces. 3.4. Picard group for primary Kodaira surfaces -- 4. Existence of holomorphic vector bundles. 4.1. Serre construction. 4.2. Filtrable vector bundles. 4.3. Non-filtrable and irreducible vector bundles. 4.4. Simple filtrable vector bundles -- 5. Classification of vector bundles. 5.1. Deformations of vector bundles and applications. 5.2. Moduli spaces of simple vector bundles. 5.3. Stable vector bundles.".
• catalog title "Holomorphic vector bundles over compact complex surfaces / Vasile Brînzănescu.".
• catalog type "text".