掃一掃
關注中圖網
官方微博
本類五星書更多>
-
>
宇宙、量子和人類心靈
-
>
氣候文明史
-
>
南極100天
-
>
考研數學專題練1200題
-
>
希格斯:“上帝粒子”的發明與發現
-
>
神農架疊層石:10多億年前遠古海洋微生物建造的大堡礁
-
>
聲音簡史
概型的幾何 版權信息
- ISBN：7510004742
- 條形碼：9787510004742 ; 978-7-5100-0474-2
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
概型的幾何 本書特色
概型理論是代數幾何的基礎，在代數幾何的經典領域不變理論和曲線模中有了較好的發展。將代數數論和代數幾何有機的結合起來，實現了早期數論學者們的愿望。這種結合使得數論中的一些主要猜測得以證明。 本書旨在建立起經典代數幾何基本教程和概型理論之間的橋梁。例子講解詳實，努力挖掘定義背后的深層次東西。練習加深讀者對內容的理解。學習本書的起點低，了解交換代數和代數變量的基本知識即可。本書揭示了概型和其他幾何觀點，如流形理論的聯系。了解這些觀點對學習本書是相當有益的，雖然不是必要。
概型的幾何 內容簡介
概型理論是代數幾何的基礎,在代數幾何的經典領域不變理論和曲線模中有了較好的發展。將代數數論和代數幾何有機的結合起來,實現了早期數論學者們的愿望。這種結合使得數論中的一些主要猜測得以證明。
本書旨在建立起經典代數幾何基本教程和概型理論之間的橋梁。例子講解詳實,努力挖掘定義背后的深層次東西。練習加深讀者對內容的理解。學習本書的起點低,了解交換代數和代數變量的基本知識即可。本書揭示了概型和其他幾何觀點,如流形理論的聯系。了解這些觀點對學習本書是相當有益的,雖然不是必要。目次:基本定義;例子;射影概型;經典結構;局部結構;概型和函子。
概型的幾何 目錄
I Basic Definitions
I.1 Affine Schemes
I.1.1 Schemes as Sets
I.1.2 Schemes as Topological Spaces
I.1.3 An Interlude on Sheaf Theory References for the Theory of Sheaves
I.1.4 Schemes as Schemes (Structure Sheaves)
I.2 Schemes in General
I.2.1 Subschemes
I.2.2 The Local Ring at a Point
I.2.3 Morphisms
I.2.4 The Gluing Construction Projective Space
I.3 Relative Schemes
I.3.1 Fibered Products
I.3.2 The Category of S-Schemes
I.3.3 Global Spec
I.4 The Functor of Points
II Examples
II.1 Reduced Schemes over Algebraically Closed Fields
II. 1.1 Affine Spaces
II.1.2 Local Schemes
II.2 Reduced Schemes over Non-Algebraically Closed Fields
II.3 Nonreduced Schemes
II.3.1 Double Points
II.3.2 Multiple Points Degree and Multiplicity
II.3.3 Embedded Points Primary Decomposition
II.3.4 Flat Families of Schemes
Limits
Examples
Flatness
II.3.5 Multiple Lines
II.4 Arithmetic Schemes
II.4.1 Spec Z
II.4.2 Spec of the Ring of Integers in a Number Field
II.4.3 Affine Spaces over Spec Z
II.4.4 A Conic over Spec Z
II.4.5 Double Points in Al
III Projective Schemes
III.1 Attributes of Morphisms
III.1.1 Finiteness Conditions
III.1.2 Properness and Separation
III.2 Proj of a Graded Ring
III.2.1 The Construction of Proj S
III.2.2 Closed Subschemes of Proj R
III.2.3 Global Proj
Proj of a Sheaf of Graded 0x-Algebras
The Projectivization P(ε) of a Coherent Sheaf ε
III.2.4 Tangent Spaces and Tangent Cones
Affine and Projective Tangent Spaces
Tangent Cones
III.2.5 Morphisms to Projective Space
III.2.6 Graded Modules and Sheaves
III.2.7 Grassmannians
III.2.8 Universal Hypersurfaces
III.3 Invariants of Projective Schemes
III.3.1 Hilbert Functions and Hilbert Polynomials
1II.3.2 Flatness Il: Families of Projective Schemes
III.3.3 Free Resolutions
III.3.4 Examples
Points in the Plane
Examples: Double Lines in General and in p3
III.3.5 BEzout's Theorem
Multiplicity of Intersections
III.3.6 Hilbert Series
IV Classical Constructions
V Local Constructions
VI Schemes and Functors
References
Index
I.1 Affine Schemes
I.1.1 Schemes as Sets
I.1.2 Schemes as Topological Spaces
I.1.3 An Interlude on Sheaf Theory References for the Theory of Sheaves
I.1.4 Schemes as Schemes (Structure Sheaves)
I.2 Schemes in General
I.2.1 Subschemes
I.2.2 The Local Ring at a Point
I.2.3 Morphisms
I.2.4 The Gluing Construction Projective Space
I.3 Relative Schemes
I.3.1 Fibered Products
I.3.2 The Category of S-Schemes
I.3.3 Global Spec
I.4 The Functor of Points
II Examples
II.1 Reduced Schemes over Algebraically Closed Fields
II. 1.1 Affine Spaces
II.1.2 Local Schemes
II.2 Reduced Schemes over Non-Algebraically Closed Fields
II.3 Nonreduced Schemes
II.3.1 Double Points
II.3.2 Multiple Points Degree and Multiplicity
II.3.3 Embedded Points Primary Decomposition
II.3.4 Flat Families of Schemes
Limits
Examples
Flatness
II.3.5 Multiple Lines
II.4 Arithmetic Schemes
II.4.1 Spec Z
II.4.2 Spec of the Ring of Integers in a Number Field
II.4.3 Affine Spaces over Spec Z
II.4.4 A Conic over Spec Z
II.4.5 Double Points in Al
III Projective Schemes
III.1 Attributes of Morphisms
III.1.1 Finiteness Conditions
III.1.2 Properness and Separation
III.2 Proj of a Graded Ring
III.2.1 The Construction of Proj S
III.2.2 Closed Subschemes of Proj R
III.2.3 Global Proj
Proj of a Sheaf of Graded 0x-Algebras
The Projectivization P(ε) of a Coherent Sheaf ε
III.2.4 Tangent Spaces and Tangent Cones
Affine and Projective Tangent Spaces
Tangent Cones
III.2.5 Morphisms to Projective Space
III.2.6 Graded Modules and Sheaves
III.2.7 Grassmannians
III.2.8 Universal Hypersurfaces
III.3 Invariants of Projective Schemes
III.3.1 Hilbert Functions and Hilbert Polynomials
1II.3.2 Flatness Il: Families of Projective Schemes
III.3.3 Free Resolutions
III.3.4 Examples
Points in the Plane
Examples: Double Lines in General and in p3
III.3.5 BEzout's Theorem
Multiplicity of Intersections
III.3.6 Hilbert Series
IV Classical Constructions
V Local Constructions
VI Schemes and Functors
References
Index
展開全部
書友推薦
- >
二體千字文
- >
中國人在烏蘇里邊疆區:歷史與人類學概述
- >
巴金－再思錄
- >
新文學天穹兩巨星--魯迅與胡適/紅燭學術叢書(紅燭學術叢書)
- >
名家帶你讀魯迅:故事新編
- >
人文閱讀與收藏·良友文學叢書:一天的工作
- >
小考拉的故事-套裝共3冊
- >
我與地壇
本類暢銷
