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Algebraic Geometry 2 - 99 edition

Algebraic Geometry 2 (ISBN10: 0821813579; ISBN13: 9780821813577)
ISBN13: 978-0821813577
ISBN10: 0821813579

Summary: Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes (see Volume 185 in the same series, Translations of Mathematical Monographs). In the present book, Ueno turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on ...show morea complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves. The primary tool in understanding sheaves is cohomology. For example, in studying ampleness, it is frequently useful to translate a property of sheaves into a statement about its cohomology. The text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as * coherent and quasicoherent sheaves. * proper and projective morphisms. * direct and inverse images. * Cech cohomology. For the mathematician unfamiliar with the language of schemes and sheaves, algebraic geometry can seem distant. However, Ueno makes the topic seem natural through his concise style and his insightful explanations. He explains why things are done this way and supplements his explanations with illuminating examples. ...show less

Edition/Copyright: 99
Cover: Paperback
Publisher: American Mathematical Society
Published: 02/12/2001
International: No



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Brand new. We distribute directly for the publisher. Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: ...show more From Algebraic Varieties to Schemes, (see Volume 185 in the same series, Translations of Mathematical Monographs). In the present book, Ueno turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves. The primary tool in understanding sheaves is cohomology. For example, in studying ampleness, it is frequently useful to translate a property of sheaves into a statement about its cohomology.The text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as ... * coherent and quasicoherent sheaves. * proper and projective morphisms. * direct and inverse images. * ????ech cohomology.For the mathematician unfamiliar with the language of schemes and sheaves, algebraic geometry can seem distant. However, Ueno makes the topic seem natural through his concise style and his insightful explanations. He explains why things are done this way and supplements his explanations with illuminating examples. As a result, he is able to make algebraic geometry very accessible to a wide audience of non-specialists.The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry. ...show less
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Michener & Rutledge Bookseller KS
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2001 Paperback Very Good 0821813579. Text clean and solid; Translations of Mathematical Monographs; 8.30 X 5.50 X 0.50 inches; 184 pages.
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2001 Trade paperback Like New Fine. No dust jacket as issued. Trade paperback (US). Glued binding. 184 p. Iwanami Series in Modern Mathematics. Audience: General/trade.
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2001 Paperback NEAR FINE This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. *****PLEASE NOTE: This item is shipping from an authorize ...show mored seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** ...show less
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