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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。
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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
……
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