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Algebraic Surfaces and Holomorphic Vector Bundles

Name: Algebraic Surfaces and Holomorphic Vector Bundles
Brand: Springer-Verlag New York Inc.
SKU: 05248158
Price: 84.09 EUR
Availability: InStock
Author: Robert Friedman
ISBN: 9780387983615

Robert Friedman

Language

English

Book Hardback

Libristo code: 05248158

Publishers Springer-Verlag New York Inc., January 1998

This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated ma... Full description

Libristo code: 05248158

206 b

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This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first year course in algebraic geometry (at the level of Hartshorne's ALGEBRAIC GEOMETRY), as well as more advanced graduate students and researchers in the areas of algebraic geometry, gauge thoery, or 4-manifold topolgogy. Many of the results on vector bundles should also be of interest to physicists studying string theory. A novel feature ofthe book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, and are studied in alternate chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, and then the geometry of vector bundles over such surfaces is analyzed. Many of the results on vector bundles appear for the first time in book form, suitable for graduate students. The book also has a strong emphasis on examples, both of surfaces and vector bundles. There are over 100 exercises which form an integral part of the text.