Holomorphic Vector Bundles over Compact Complex Surfaces
Brînzănescu, Vasile.
Holomorphic Vector Bundles over Compact Complex Surfaces [electronic resource] / by Vasile Brînzănescu. - X, 178 p. online resource. - Lecture Notes in Mathematics, 1624 0075-8434 ; . - Lecture Notes in Mathematics, 1624 .
Vector bundles over complex manifolds -- Facts on compact complex surfaces -- Line bundles over surfaces -- Existence of holomorphic vector bundles -- Classification of vector bundles.
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.
9783540498452
10.1007/BFb0093696 doi
Global differential geometry.
Algebraic topology.
Geometry.
Geometry, algebraic.
Differential Geometry.
Algebraic Topology.
Geometry.
Algebraic Geometry.
QA641-670
516.36
Holomorphic Vector Bundles over Compact Complex Surfaces [electronic resource] / by Vasile Brînzănescu. - X, 178 p. online resource. - Lecture Notes in Mathematics, 1624 0075-8434 ; . - Lecture Notes in Mathematics, 1624 .
Vector bundles over complex manifolds -- Facts on compact complex surfaces -- Line bundles over surfaces -- Existence of holomorphic vector bundles -- Classification of vector bundles.
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.
9783540498452
10.1007/BFb0093696 doi
Global differential geometry.
Algebraic topology.
Geometry.
Geometry, algebraic.
Differential Geometry.
Algebraic Topology.
Geometry.
Algebraic Geometry.
QA641-670
516.36