《Topological Methods in Algebraic Geometry (Classics in Mathematics)》是德國數學家弗里德里希·赫茨布魯赫（Friedrich Hirzebruch）的學術著作，由Springer出版社於1995年2月出版，隸屬"Classics in Mathematics"叢書系列，全書共252頁，平裝本定價49.95美元。該書基於作者1952-1954年在普林斯頓高等研究院與K. Kodaira、D.C. Spencer的合作研究成果，系統梳理了拓撲方法在代數幾何領域的理論發展。
本書重點闡述層論在多複變函數論與代數幾何中的套用，收錄H. Cartan和J.-P. Serre關於Stein流形的基本定理的層論表述，以及K. Kodaira和D.C. Spencer採用調和積分等微分幾何技術的研究成果。同時包含M.F. Atiyah與W.V.D. Hodge運用層論處理代數流形第二類積分問題的經典工作。書中內容涵蓋Todd虧格、代數流形黎曼-羅赫定理等核心理論框架，展現了20世紀中葉代數幾何與拓撲學交叉研究的代表性進展。
基本介紹
- ISBN：9783540586630
- 作者：Friedrich Hirzebruch
- 出版社：Springer
- 出版時間：1995年2月24日
- 頁數：252
- 定價：USD 49.95
- 裝幀：Paperback
- 叢書：Classics in Mathematics
內容簡介
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 t...(展開全部) 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.
