Graduate Texts in Mathematics: Algebraic Geometry: A First Course (Hardback)

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LIKE NEW: These books are in excellent, like-new condition. They were printed on acid-free paper.

Product Details

These are Volume 133 in Springer'sGraduate 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 Lectures

1. Affine and Projective Varieties
2. Regular Functions and Maps
3. Cones, Projections, and More About Products
4. Families and Parameter Spaces
5. Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz
6. Grassmannians and Related Varieties
7. Rational Functions and Rational Maps
8. More Examples
9. Determinantal Varieties
10. Algebraic Groups

Part II: Attributes of Varieties Lectures

11. Definitions of Dimension and Elementary Examples
12. More Dimension Computations
13. Hilbert Polynomials
14. Smoothness and Tangent Spaces
15. Gauss Maps, Tangential and Dual Varieties
16. Tangent Spaces to Grassmannians
17. Further Topics Involving Smoothness and Tangent Spaces
18. Degree
19. Further Examples and Applications of Degree
20. Singular Points and Tangent Cones
21. Parameter Spaces and Moduli Spaces
22. Quadrics

The text ends with "Hints for Selected Exercises," "References," and "Index."