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.
General
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