新書推薦:

《
替代式创新:关键核心技术突破的中国式路径
》
售價:NT$
454

《
阴郁之人的晴朗之地
》
售價:NT$
316

《
金融陷阱
》
售價:NT$
352

《
豆包AI从会用到精通
》
售價:NT$
296

《
HR必备法律工具书:企业用工风险防范实务操作与案例精解(第二版)
》
售價:NT$
551

《
威尔·杜兰特:最伟大的思想
》
售價:NT$
245

《
日本装帧110年系谱
》
售價:NT$
806

《
厨房药房:用香料和药草疗愈身心
》
售價:NT$
254
|
| 內容簡介: |
|
This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries.Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners.《代数几何基础教程(英文版)》为英文版。
|
| 目錄:
|
Preface
Acknowledgments
Using This Book
PART Ⅰ:EXAMPLES OF VARIETIES AND MAPS
LECTURE 1 Affine and Projective Varieties
A Note About Our Field
Affine Space andAffineVarieties
Projective Space and Projective Varieties
Linear Spaces
Finite Sets
Hypersurfaces
Analytic Subvarieties and Submanifolds
The Twisted Cubic
Rational Normal Curves
Determinantai Representation of the Rational Normal Curve
Another Parametrization of the Rational Normal Curve
The Family of Plane Conics
A Synthetic Construction of the Rational Normal Curve
0ther Rational Curves
Varieties Defined over Subfields of K
A Note on Dimension,Smoothness,and Degree
LECTURE 2 Regular Functions and Maps
The Zariski Topology
Regular Functions on an Affine Variety
Projective Varieties
Regular Maps
The Veronese Map
Determinantal ReDresentatiOn of Veronese Varieties
Subvarieties of Veronese Varieties
The Segre Maps
Subvarieties of Segre Varieties
Products of Varieties
Graphs
Fiber Products
Combinations of Veronese and Segre Maps
LECTURE 3 Cones,Projections,and More About Products
Cones
Quadrics
Projections
M0re Cones
More Projections
Constructible Sets
LECTURE 4 Families and Parameter Spaces
Families of Varieties
The Universal Hyperplane
The Universal Hyperplane Section
Parameter Spaces of Hypersurfaces
Universal Families of Hypersurfaces
A Family of Lines
……
|
|