标题：国外数学名著系列46:代数几何5
图书信息
出版社: 科学出版社; 第1版 (2009年1月1日)
丛书名: 国外数学名著系列（续一）（影印版）46
精装: 245页
正文语种: 英语
开本: 16
ISBN: 9787030234896
条形码: 9787030234896
尺寸: 24 x 16.6 x 1.8 cm
重量: 558 g
作者简介
作者：(俄罗斯)帕尔申 (Parshin A.N.)
内容简介
《国外数学名著系列(续1)(影印版)46:代数几何5(Fano簇)》 will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.The aim of this survey, written by V. A. lskovskikh and Yu. G.Prokhorov, is to provide an exposition of the structure theory of Fano varieties, i.e. algebraic varieties with an ample anticanonical divisor.Such varieties naturally appear in the birational classification of varieties of negative Kodaira dimension, and they are very close to rational ones. This EMS volume covers different approaches to the classification of Fano varieties such as the classical Fanolskovskikh"double projection"method and its modifications,the vector bundles method due to S. Mukai, and the method of extremal rays. The authors discuss uniruledness and rational connectedness as well as recent progress in rationality problems of Fano varieties. The appendix contains tables of some classes of Fano varieties.
目录
Introduction
Chapter 1. Preliminaries
1.1. Singularities
1.2. On Numerical Geometry of Cycles
1.3. On the Mori Minimal Model Program
1.4. Results on Minimal Models in Dimension Three
Chapter 2. Basic Properties of Fano Varieties
2.1. Definitions, Examples and the Simplest Properties
2.2. Some General Results
2.3. Existence of Good Divisors in the Fundamental Linear System
2.4. Base Points in the Fundamental Linear System
Chapter 3. Del Pezzo Varieties and Fano Varieties of Large Index
3.1. On Some Preliminary Results of Fujita
3.2. Del Pezzo Varieties. Definition and Preliminary Results
3.3. Nonsingular del Pezzo Varieties. Statement of the Main Theorem and Beginning of the Proof
3.4. Del Pezzo Varieties with Picard Number p = 1.
Continuation of the Proof of the Main Theorem
3.5. Del Pezzo Varieties with Picard Number p ≥ 2.
Conclusion of the Proof of the Main Theorem
Chapter 4. Fano Threefolds with p = 1
4.1. Elementary Rational Maps: Preliminary Results
4.2. Families of Lines and Conics on Fano Threefolds
4.3. Elementary Rational Maps with Center along a Line
4.4. Elementary Rational Maps with Center along a Conic
4.5. Elementary Rational Maps with Center at a Point
4.6. Some Other Rational Maps
Chapter 5. Fano Varieties of Coindex 3 with p = 1:
The Vector Bundle Method
5.1. Fano Threefolds of Genus 6 and 8: Gushel's Approach
5.2. A Review of Mukai's Results on the Classification of Fano Manifolds of Coindex 3
Chapter 6. Boundedness and Rational Connectedness of Fano Varieties
6.1. Uniruledness
6.2. Rational Connectedness of Fano Varieties
Chapter 7. Fano Varieties with p ≥ 2
7.1. Fano Threefolds with Picard Number p ≥ 2 (Survey of Results of Mori and Mukai
7.2. A Survey of Results about Higher-dimensional Fano Varieties with Picard Number p ≥ 2
Chapter 8. Rationality Questions for Fano Varieties I
8.1. Intermediate Jacobian and Prym Varieties
8.2. Intermediate Jacobian: the Abel-Jacobi Map
8.3. The Brauer Group as a Birational Invariant
Chapter 9. Rationality Questions for Fano Varieties II
9.1. Birational Automorphisms of Fano Varieties
9.2. Decomposition of Birational Maps in the Context of Mori Theory
Chapter 10. Some General Constructions of Rationality and Unirationality
10.1. Some Constructions of Unirationality
10.2. Unirationality of Complete Intersections
10.3. Some General Constructions of Rationality
Chapter 11. Some Particular Results and Open Problems
11.1. On the Classification of Three-dimensional -Fano Varieties
11.2. Generalizations
11.3. Some Particular Results
11.4. Some Open Problems
Chapter 12. Appendix: Tables
12.1. Del Pezzo Manifolds
12.2. Fano Threefolds with p = 1
12.3. Fano Threefolds with p = 2
12.4. Fano Threefolds with p = 3
12.5. Fano Threefolds with p = 4
12.6. Fano Threefolds with p ≥ 5
12.7. Fano Fourfolds of Index 2 with p ≥ 2
12.8. Toric Fano Threefolds
References
Index     

图书信息
出版社: 世界图书出版公司; 第1版 (2011年4月1日)
外文书名: A Panoramic View of Riemannian Geometry
平装: 824页
开本: 24
ISBN: 9787510033063
条形码: 9787510033063
尺寸: 22 x 14.8 x 3.6 cm
重量: 1.1 Kg
作者简介
作者:(法)贝格
目录
1  Euclidean Geometry 
2  Transition 
3  Surfaces from Gaufi to Today 
4  Riemann's Blueprints 
5  A one Page Panorama 
6  Metric Geometry and Curvature 
7  Volumes and Inequalities on Volumes of Cycles 
8  Transition: The Next Two Chapters
9  Spectrum of The Laplacian 
10  Geodesic Dynamics 
11  Best Metrics
12  From Curvature to Topology
13  Holonomy Groups and Kahler Manifolds
14  Some Other Important Topics
15  The Technical Chapter
References
Acknowledgements
List of Notation
List of Authors
Subject Index