Algebraic Geometry: Sheaves and Cohomology v.2: Sheaves and Cohomology Vol 2 (Translations of Mathematical Monographs) - Softcover

Softcover

ISBN 10: 0821813579 ISBN 13: 9780821813577

Publisher: American Mathematical Society, 2001

Synopsis

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 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. 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. 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.

About this title

Review

... this book is an excellent instructional exposition for an introduction to algebraic geometry. (Mathematical Reviews )

Edition details

• Publisher: American Mathematical Society
• Publication date: 2001
• Language: English
• ISBN 10: 0821813579
• ISBN 13: 9780821813577
• Binding: Paperback
• Number of pages: 200
• Editor: Ueno Kenji