Algebraic geometry : a first course /
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 emplasizes the classical roots of the subject. For readers interested in simply seeing wh...
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer-Verlag,
[1992]
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| Series: | Graduate texts in mathematics ;
133. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Pt. I. 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
- Pt. 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.