By Robert Friedman

A singular characteristic of the booklet is its built-in method of algebraic floor idea and the research of vector package deal concept on either curves and surfaces. whereas the 2 topics stay separate during the first few chapters, they develop into even more tightly interconnected because the ebook progresses. therefore vector bundles over curves are studied to appreciate governed surfaces, after which reappear within the evidence of Bogomolov's inequality for sturdy bundles, that's itself utilized to review canonical embeddings of surfaces through Reider's approach. equally, governed and elliptic surfaces are mentioned intimately, earlier than the geometry of vector bundles over such surfaces is analysed. some of the effects on vector bundles look for the 1st time in ebook shape, subsidized via many examples, either one of surfaces and vector bundles, and over a hundred workouts forming a vital part of the textual content. aimed toward graduates with an intensive first-year direction in algebraic geometry, in addition to extra complex scholars and researchers within the components of algebraic geometry, gauge concept, or 4-manifold topology, the various effects on vector bundles can be of curiosity to physicists learning string concept.

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