This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first year course in algebraic geometry (at the level of Hartshorne's ALGEBRAIC GEOMETRY), as well as more advanced graduate students and researchers in the areas of algebraic geometry, gauge thoery, or 4-manifold topolgogy. Many of the results on vector bundles should also be of interest to physicists studying string theory. A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, and are studied in alternate chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, and then the geometry of vector bundles over such surfaces is analyzed. Many of the results on vector bundles appear for the first time in book form, suitable for graduate students. The book also has a strong emphasis on examples, both of surfaces and vector bundles. There are over 100 exercises which form an integral part of the text.
發表於2024-12-25
Algebraic Surfaces and Holomorphic Vector Bundles (Universitext) 2024 pdf epub mobi 電子書 下載
陳類(Chern class)是幾何拓撲中的一個非常重要的不變量,不僅定義相對比較復雜,具體計算也有一定的技巧性,下麵我們就從代數幾何的角度討論一下相關問題。 在代數幾何中,陳類一般是先定義在綫束(line bundle)上,然後再推廣到一般嚮量束(vector bundle,中...
評分陳類(Chern class)是幾何拓撲中的一個非常重要的不變量,不僅定義相對比較復雜,具體計算也有一定的技巧性,下麵我們就從代數幾何的角度討論一下相關問題。 在代數幾何中,陳類一般是先定義在綫束(line bundle)上,然後再推廣到一般嚮量束(vector bundle,中...
評分陳類(Chern class)是幾何拓撲中的一個非常重要的不變量,不僅定義相對比較復雜,具體計算也有一定的技巧性,下麵我們就從代數幾何的角度討論一下相關問題。 在代數幾何中,陳類一般是先定義在綫束(line bundle)上,然後再推廣到一般嚮量束(vector bundle,中...
評分陳類(Chern class)是幾何拓撲中的一個非常重要的不變量,不僅定義相對比較復雜,具體計算也有一定的技巧性,下麵我們就從代數幾何的角度討論一下相關問題。 在代數幾何中,陳類一般是先定義在綫束(line bundle)上,然後再推廣到一般嚮量束(vector bundle,中...
評分陳類(Chern class)是幾何拓撲中的一個非常重要的不變量,不僅定義相對比較復雜,具體計算也有一定的技巧性,下麵我們就從代數幾何的角度討論一下相關問題。 在代數幾何中,陳類一般是先定義在綫束(line bundle)上,然後再推廣到一般嚮量束(vector bundle,中...
圖書標籤: 數學 代數幾何7 ma
此書的編排很有意思,一三五七講surface,二四六八講bundle,最後兩章的順序是不是該顛倒一下啊?
評分作為《Principles in Algebraic Geometry》的對照閱讀
評分此書的編排很有意思,一三五七講surface,二四六八講bundle,最後兩章的順序是不是該顛倒一下啊?
評分此書的編排很有意思,一三五七講surface,二四六八講bundle,最後兩章的順序是不是該顛倒一下啊?
評分作為《Principles in Algebraic Geometry》的對照閱讀
Algebraic Surfaces and Holomorphic Vector Bundles (Universitext) 2024 pdf epub mobi 電子書 下載