Algebraic and Analytic Geometry pdf epub mobi txt 电子书下载 2025

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出版者:Cambridge University Press

作者:Amnon Neeman

出品人:

页数:434

译者:

出版时间:2007-9-24

价格:USD 88.99

装帧:Paperback

isbn号码:9780521709835

丛书系列:London Mathematical Society Lecture Note Series

图书标签:

代数几何
数学
复几何
mathematics
复分析7
复几何7
QS
MathGeometry

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This textbook, for an undergraduate course in modern algebraic geometry, recognizes that the typical undergraduate curriculum contains a great deal of analysis and, by contrast, little algebra. Because of this imbalance, it seems most natural to present algebraic geometry by highlighting the way it connects algebra and analysis; the average student will probably be more familiar and more comfortable with the analytic component. The book therefore focuses on Serre's GAGA theorem, which perhaps best encapsulates the link between algebra and analysis. GAGA provides the unifying theme of the book: we develop enough of the modern machinery of algebraic geometry to be able to give an essentially complete proof, at a level accessible to undergraduates throughout. The book is based on a course which the author has taught, twice, at the Australian National University.

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本书只证明的一个关键定理就是serre的GAGA：从代数范畴多项式（整体）到其解析范畴（局部问题）之间的类比关系。有限概型上的三个对象代数和分析等价：闭子集，向量丛，映射（代数丛上的映射是全纯的）紧性条件下。概型可以看做为流形或者是簇的推广（流形-环层空间-局部环层空间-素谱-概型局部模型是仿射概型）。层是整体定义的，但本质是局部的。可微流形的本质是拓扑流形加上了可微函数组成的向量空间=环层（X，Ox）

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