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聲音簡(jiǎn)史
概型的幾何 版權(quán)信息
- ISBN:7510004742
- 條形碼:9787510004742 ; 978-7-5100-0474-2
- 裝幀:一般膠版紙
- 冊(cè)數(shù):暫無(wú)
- 重量:暫無(wú)
- 所屬分類(lèi):>>
概型的幾何 本書(shū)特色
概型理論是代數(shù)幾何的基礎(chǔ),在代數(shù)幾何的經(jīng)典領(lǐng)域不變理論和曲線模中有了較好的發(fā)展。將代數(shù)數(shù)論和代數(shù)幾何有機(jī)的結(jié)合起來(lái),實(shí)現(xiàn)了早期數(shù)論學(xué)者們的愿望。這種結(jié)合使得數(shù)論中的一些主要猜測(cè)得以證明。 本書(shū)旨在建立起經(jīng)典代數(shù)幾何基本教程和概型理論之間的橋梁。例子講解詳實(shí),努力挖掘定義背后的深層次東西。練習(xí)加深讀者對(duì)內(nèi)容的理解。學(xué)習(xí)本書(shū)的起點(diǎn)低,了解交換代數(shù)和代數(shù)變量的基本知識(shí)即可。本書(shū)揭示了概型和其他幾何觀點(diǎn),如流形理論的聯(lián)系。了解這些觀點(diǎn)對(duì)學(xué)習(xí)本書(shū)是相當(dāng)有益的,雖然不是必要。
概型的幾何 內(nèi)容簡(jiǎn)介
概型理論是代數(shù)幾何的基礎(chǔ),在代數(shù)幾何的經(jīng)典領(lǐng)域不變理論和曲線模中有了較好的發(fā)展。將代數(shù)數(shù)論和代數(shù)幾何有機(jī)的結(jié)合起來(lái),實(shí)現(xiàn)了早期數(shù)論學(xué)者們的愿望。這種結(jié)合使得數(shù)論中的一些主要猜測(cè)得以證明。
本書(shū)旨在建立起經(jīng)典代數(shù)幾何基本教程和概型理論之間的橋梁。例子講解詳實(shí),努力挖掘定義背后的深層次東西。練習(xí)加深讀者對(duì)內(nèi)容的理解。學(xué)習(xí)本書(shū)的起點(diǎn)低,了解交換代數(shù)和代數(shù)變量的基本知識(shí)即可。本書(shū)揭示了概型和其他幾何觀點(diǎn),如流形理論的聯(lián)系。了解這些觀點(diǎn)對(duì)學(xué)習(xí)本書(shū)是相當(dāng)有益的,雖然不是必要。目次:基本定義;例子;射影概型;經(jīng)典結(jié)構(gòu);局部結(jié)構(gòu);概型和函子。
概型的幾何 目錄
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
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