About the Book

This book is intended to introduce students to algebraic geometry; to give them a sense of the basic objects
considered, the questions asked about them, and the sort of answers one can expect to obtain. It thus emphasises the classical roots of the subject. For readers interested in simply seeing what the subject is about, this avoids the more technical details better treated with the most recent methods. For readers
interested in pursuing the subject further, this book will provide a basis for understanding the developments of the last half century, which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard Universities, this book retains the informal style of the lectures and stresses examples throughout; the theory is developed as needed. The first part is concerned with introducing basic varieties and constructions; it describes, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic
groups. The second part discusses attributes of varieties, including dimension, smoothness, tangent spaces
and cones, degree, and parameter and moduli spaces.