"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS
Table of ContentsI: 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.- 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 Quadrics.- Hints for Selected Exercises.- References.