代数几何中的拓扑方法 2024 pdf epub mobi 电子书

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发表于2024-12-22

代数几何中的拓扑方法 2024 pdf epub mobi 电子书

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出版者:北京世界图书出版公司

作者:Friedrich Hirzebruch

出品人:

页数:234

译者:

出版时间:2004-11

价格:39.00元

装帧:

isbn号码:9787506271875

丛书系列:Classics in Mathematics

图书标签: 代数几何数学几何与拓扑拓扑经典拓扑学大师代数几何7

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In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954.

代数几何中的拓扑方法 2024 pdf epub mobi 电子书

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Thom定理：低维闭流形是高维流形的边缘（映射的像）那么低维闭流形的不变量定义为高维流形的指标和庞特里亚金类的多项式。Hirzebruch通过托姆配边定理证明了流形的指标是庞特里亚金类的多项式的假设，然后就得到了高维的黎曼罗赫定理。格罗滕迪克代数化了这个定理得到了簇间的黎曼罗赫定理（簇间映射分解为投影和嵌入的形变）。博特和阿蒂亚通过整性概念的引导借鉴了Lefschetz 复解析流形不动点定理，得到了李群外尔特征公式

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