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ISBN: 0792351541 9780792351542 Year: 1998 Publisher: Dordrecht: Kluwer Academic Publishers,
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ISBN: 0387983619 Year: 1998 Publisher: New York : Springer,
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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 theory, or 4-manifold topology. Many of the results on vector bundles should also be of interest to physicists studying string theory. A novel feature of the 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.
Surfaces, Algebraic --- Vector bundles --- Surfaces algebriques --- Fibrés vectoriels
ISBN: 2800126442 Year: 1998 Publisher: Marcinelle Dupuis
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ISBN: 3540645381 3540698043 9783540645382 Year: 1998 Volume: 1689 Publisher: Berlin Springer
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Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.
Differential geometry. Global analysis --- Schubert varieties --- Intersection theory --- Vector bundles --- Intersection theory (Mathematics) --- Geometry --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Algebraic geometry. --- Combinatorics. --- Group theory. --- Algebraic topology. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Algebraic Topology. --- Topology --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Combinatorics --- Mathematical analysis --- Algebraic geometry --- Schubert varieties. --- Vector bundles. --- Fiber spaces (Mathematics) --- Geometry, Algebraic
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