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A royal road to algebraic geometry

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概要 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 le...arning 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.続きを見る
目次 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.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2012 English/International

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登録日 2020.06.27
更新日 2020.06.28

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