A royal road to algebraic geometry / Audun Holme
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Heidelberg ; New York : Springer |
| 出版年 | c2012 |
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| 書誌ID | OB01027632 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | "Creative episodes in its history"-P.4 of cover Includes bibliographical references and index Pt. I: Curves -- 1. Affine and Projective Space -- 2. Curves in A² [subscript k] and in P² [subscript k] -- 3. Higher Geometry in the Projective Plane -- 4. Plane Curves and Algebra -- 5. Projective Varieties in P [ superscript] N [subscript] k -- Pt. II: Introduction to Grothendieck's Theory of Schemes -- 6. Categories and Functors -- 7. Constructions and Representable -- 8. Abelian Categories -- 9. The Concept of Spec(A) -- 10. The Category of Schemes -- 11. Properties of Morphisms of Schemes -- 12. Modules, Algebras and Bundles on a. Scheme -- 13. More Properties of Morphisms, Scheme Theoretic Image and the "Sorite" -- 14. Projective Schemes and Bundles -- 15. Further Properties of Morphisms -- 16. Conormal Sheaf and Projective Bundles -- 17. Cohomology Theory on Schemes -- 18. Intersection Theory -- 19. Characteristic Classes in Algebraic Geometry -- 20. The Riemann-Roch Theorem -- 21. Some Basic Constructions in the Category of Projective k--- 22. More on Duality. License restrictions may limit access This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: "There is no royal road to geometry!" The book starts by explaining this enigmatic answer, the aim of the book being to ague that indeed, in some sense there is a royal road to algebraic geometry. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck's theory of schemes. Contemporary homological tools are explained. The reader will follow a directed path leading up to the main elements of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest scientific experience of a lifetime!--P. 4 of cover |
| 著者標目 | *Holme, Audun |
| 件 名 | LCSH:Geometry, Algebraic LCSH:Curves, Algebraic LCSH:Categories (Mathematics) LCSH:Algebra, Homological |
| 分 類 | LCC:QA564 DC22:516 |
| 巻冊次 | hdbk. : acid-free paper ; ISBN:9783642192241 RefWorks出力（各巻） hdbk. : acid-free paper ; ISBN:3642192246 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
| 所蔵情報へのリンク | A royal road to algebraic geometry / Audun Holme ; : hbk |
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※2020年8月16日以降