代数几何基础教程

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		代数几何基础教程
		代数几何基础教程

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.

　　本书为英文版。

编辑推荐

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.

目录

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

网友对代数几何基础教程的评论

有丰富的例子，可以帮助建立直观，但需要花很多时间学并且只讲了variety。

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