代数几何基础教程

出版时间：2000-6  出版社：世界图书出版公司  作者：J.Harris  页数：328  
Tag标签：无  

内容概要

　　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.

书籍目录

PrefaceAcknowledgmentsUsing This BookPART I: EXAMPLES OF VARIETIES AND MAPSLECTURE 1 Affine and Projective VarietiesLECTURE 2 Regular Functions and MapsLECTURE 3 Cones, Projections, and More About ProductsLECTURE 4 Families and Parameter SpacesLECTURE 5 Ideals of Varieties, Irreducible Decomposition, and the NullstellensatzLECTURE 6 Grassmannians and Related VarietiesLECTURE 7 Rational Functions and Rational MapsLECTURE 8 More ExamplesLECTURE 9 Determinantal VarietiesLECTURE 10 Algebraic GroupsPART II: ATTRIBUTES OF VARIETIESLECTURE 11 Definitions of Dimension and Elementary ExamplesLECTURE 12 More Dimension ComputationsLECTURE 13 Hilbert PolynomialsLECTURE 14 Smoothness and Tangent SpacesLECTURE 15 Gauss Maps, Tangential and Dual VarietiesLECTURE 16 Tangent Spaces to GrassmanniansLECTURE 17 Further Topics Involving Smoothness and Tangent SpacesLECTURE 18 DegreeLECTURE 19 Further Examples and Applications of DegreeLECTURE 20 Singular Points and Tangent ConesLECTURE 21 Parameter Spaces and Moduli SpacesLECTURE 22 QuadricsHints for Selected ExercisesReferencesIndex