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Graduate Texts in Mathematics: Algebraic Geometry: A First Course (Hardback)
"These books are 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 emphasizes the classical roots of the subject." — From the back cover
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LIKE NEW: These books are in excellent, like-new condition. They were printed on acid-free paper.
These are Volume 133 in Springer’s Graduate Texts in Mathematics series.
Continued from the back cover: “For readers interested in simply seeing what the subject is about, this book 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.”
Part I: Examples of Varieties and Maps
- Affine and Projective Varieties
- Regular Functions and Maps
- Cones, Projections, and More About Products
- Families and Parameter Spaces
- Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz
- Grassmannians and Related Varieties
- Rational Functions and Rational Maps
- More Examples
- Determinantal Varieties
- Algebraic Groups
Part II: Attributes of Varieties
- Definitions of Dimension and Elementary Examples
- More Dimension Computations
- Hilbert Polynomials
- Smoothness and Tangent Spaces
- Gauss Maps, Tangential and Dual Varieties
- Tangent Spaces to Grassmannians
- Further Topics Involving Smoothness and Tangent Spaces
- Further Examples and Applications of Degree
- Singular Points and Tangent Cones
- Parameter Spaces and Moduli Spaces
The text ends with “Hints for Selected Exercises,” “References,” and “Index.”
- Harris, Joe
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- Springer Graduate Texts in Mathematics
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