图书介绍
判别式、结式和多维行列式 英文PDF|Epub|txt|kindle电子书版本下载
- 盖尔芬德（GelfandI.M.）著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：7510061455
- 出版时间：2013
- 标注页数：523页
- 文件大小：68MB
- 文件页数：536页
- 主题词：
PDF下载
下载说明
判别式、结式和多维行列式 英文PDF格式电子书版下载
下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！
（文件页数 要大于 标注页数，上中下等多册电子书除外）
注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具
图书目录
Introduction1
Ⅰ．GENERAL DISCRIMINANTS AND RESULTANTS13
CHAPTER 1．Projective Dual Varieties and General Discriminants13
1．Definitions and basic examples13
2．Duality for plane curves16
3．The incidence variety and the proof of the biduality theorem27
4．Further examples and properties of projective duality30
5．The Katz dimension formula and its applications39
CHAPTER 2．The Cayley Method for Studying Discriminants48
1．Jet bundles and Koszul complexes48
2．Discriminantal complexes54
3．The degree and the dimension of the dual61
4．Discriminantal complexes in terms of differential forms71
5．The discriminant as the determinant of a spectral sequence80
CHAPTER 3．Associated Varieties and General Resultants91
1．Grassmannians.Preliminary material91
2．Associated hypersurfaces97
3．Mixed resultants105
4．The Cayley method for the study of resultants112
CHAPTER 4．Chow Varieties122
1．Definitions and main properties122
2．O-cycles,factorizable forms and symmetric products131
3．Cayley-Green-Morrison equations of Chow varieties146
Ⅱ．A-DISCRIMINANTS AND A-RESULTANTS165
CHAPTER 5．Toric Varieties165
1．Projectively embedded toric varieties165
2．Affine toric varieties and semigroups172
3．Local structure of toric varieties177
4．Abstract toric varieties and fans187
CHAPTER 6．Newton Polytopes and Chow Polytopes193
1．Polynomials and their Newton polytopes193
2．Theorems of Kouchnirenko and Bernstein on the number of solutions of a system of equations200
3．Chow polytopes206
CHAPTER 7．Triangulations and Secondary Polytopes214
1．Triangulations and secondary polytopes214
2．Faces of the secondary polytope227
3．Examples of secondary polytopes233
CHAPTER 8．A-Resultants and Chow Polytopes of Toric Varieties252
1．Mixed(Al,...,Ak)-resultants252
2．The A-resultant255
3．The Chow polytope of a toric variety and the secondary polytope259
CHAPTER 9．A-Discriminants271
1．Basic definitions and examples271
2．The discriminantal complex275
3．A differential-geometric characterization of A-discriminantal hypersurfaces285
CHAPTER 10．Principal A-Determinants297
1．Statements of main results297
2．Proof of the prime factorization theorem313
3．Proof of the properties of generalized A-determinants329
4．The proof of the product formula333
CHAPTER 11．Regular A-Determinants and A-Discriminants344
1．Differential forms on a singular toric variety and the regular A-determinant344
2．Newton numbers and Newton functions351
3．The Newton polytope of the regular A-determinant and D-equivalence of triangulations361
4．More on D-equivalence370
5．Relations to real algebraic geometry378
Ⅲ．CLASSICAL DISCRIMINANTS AND RESULTANTS397
CHAPTER 12．Discriminants and Resultants for Polynomials in One Variable397
1．An overview of classical formulas and properties397
2．Newton polytopes of the classical discriminant and resultant411
CHAPTER 13．Discriminants and Resultants for Forms in Several Variables426
1．Homogeneous forms in several variables426
2．Forms in several groups of variables437
CHAPTER 14．Hyperdeterminants444
1．Basic properties of the hyperdeterminant444
2．The Cayley method and the degree450
3．Hyperdeterminant of the boundary format458
4．Schl？fli's method475
APPENDIX A．Determinants of Complexes480
APPENDIX B．A.Cayley:On the Theory of Elimination498
Bibliography503
Notes and References513
List of Notations517
Index521