《基礎代數幾何（第1卷）》是1998年北京世界圖書出版公司出版的圖書，作者是I.R.Shafarevich。
基本介紹
- 書名：基礎代數幾何（第1卷）
- 作者：I.R.Shafarevich
- ISBN：9787506236195
- 頁數：302
- 定價：48.00元
- 出版社：北京世界圖書出版公司
- 出版時間：1998-3
內容簡介,目錄,
內容簡介
The first edition of this book came out just as the apparatus of algebraic geometry was reaching a stage that permitted a lucid and concise account of the foundations of the subject. The author was no longer forced into the painful choice between sacrificing rigour of exposition or overloading the clear geometrical picture with cumbersome algebraic apparatus.
此書為英文版！
目錄
Preface
Acknowledgments
Using This Book
PART I: EXAMPLES OF VARIETIES AND MAPS
LECTURE 1 Affine and Projective Varieties
LECTURE 2 Regular Functions and Maps
LECTURE 3 Cones, Projections, and More About Products
LECTURE 4 Families and Parameter Spaces
LECTURE 5 Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz
LECTURE 6 Grassmannians and Related Varieties
LECTURE 7 Rational Functions and Rational Maps
LECTURE 8 More Examples
LECTURE 9 Determinantal Varieties
LECTURE 10 Algebraic Groups
PART II: ATTRIBUTES OF VARIETIES
LECTURE 11 Definitions of Dimension and Elementary Examples
LECTURE 12 More Dimension Computations
LECTURE 13 Hilbert Polynomials
LECTURE 14 Smoothness and Tangent Spaces
LECTURE 15 Gauss Maps, Tangential and Dual Varieties
LECTURE 16 Tangent Spaces to Grassmannians
LECTURE 17 Further Topics Involving Smoothness and Tangent Spaces
LECTURE 18 Degree
LECTURE 19 Further Examples and Applications of Degree
LECTURE 20 Singular Points and Tangent Cones
LECTURE 21 Parameter Spaces and Moduli Spaces
LECTURE 22 QuadricsHints for Selected Exercises
References
Index
Acknowledgments
Using This Book
PART I: EXAMPLES OF VARIETIES AND MAPS
LECTURE 1 Affine and Projective Varieties
LECTURE 2 Regular Functions and Maps
LECTURE 3 Cones, Projections, and More About Products
LECTURE 4 Families and Parameter Spaces
LECTURE 5 Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz
LECTURE 6 Grassmannians and Related Varieties
LECTURE 7 Rational Functions and Rational Maps
LECTURE 8 More Examples
LECTURE 9 Determinantal Varieties
LECTURE 10 Algebraic Groups
PART II: ATTRIBUTES OF VARIETIES
LECTURE 11 Definitions of Dimension and Elementary Examples
LECTURE 12 More Dimension Computations
LECTURE 13 Hilbert Polynomials
LECTURE 14 Smoothness and Tangent Spaces
LECTURE 15 Gauss Maps, Tangential and Dual Varieties
LECTURE 16 Tangent Spaces to Grassmannians
LECTURE 17 Further Topics Involving Smoothness and Tangent Spaces
LECTURE 18 Degree
LECTURE 19 Further Examples and Applications of Degree
LECTURE 20 Singular Points and Tangent Cones
LECTURE 21 Parameter Spaces and Moduli Spaces
LECTURE 22 QuadricsHints for Selected Exercises
References
Index
