Algebraic geometry : a first course / Joe Harris.
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...
Saved in:
| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer-Verlag,
[1992]
|
| Series: | Graduate texts in mathematics ;
133. |
| Subjects: |
MARC
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| 100 | 1 | |a Harris, Joe, |d 1951- |0 http://id.loc.gov/authorities/names/n83203184 |1 http://isni.org/isni/0000000114969558. | |
| 245 | 1 | 0 | |a Algebraic geometry : |b a first course / |c Joe Harris. |
| 264 | 1 | |a New York : |b Springer-Verlag, |c [1992] | |
| 264 | 4 | |c ©1992. | |
| 300 | |a 1 online resource (xix, 328 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
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| 490 | 1 | |a Graduate texts in mathematics ; |v 133. | |
| 504 | |a Includes bibliographical references (pages 314-315) and index. | ||
| 505 | 0 | 0 | |g pt. I. |t Examples of Varieties and Maps -- |g Lecture 1. |t Affine and Projective Varieties -- |g Lecture 2. |t Regular Functions and Maps -- |g Lecture 3. |t Cones, Projections, and More About Products -- |g Lecture 4. |t Families and Parameter Spaces -- |g Lecture 5. |t Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz -- |g Lecture 6. |t Grassmannians and Related Varieties -- |g Lecture 7. |t Rational Functions and Rational Maps -- |g Lecture 8. |t More Examples -- |g Lecture 9. |t Determinantal Varieties -- |g Lecture 10. |t Algebraic Groups -- |g pt. II. |t Attributes of Varieties -- |g Lecture 11. |t Definitions of Dimension and Elementary Examples -- |g Lecture 12. |t More Dimension Computations -- |g Lecture 13. |t Hilbert Polynomials -- |g Lecture 14. |t Smoothness and Tangent Spaces -- |g Lecture 15. |t Gauss Maps, Tangential and Dual Varieties -- |g Lecture 16. |t Tangent Spaces to Grassmannians -- |g Lecture 17. |t Further Topics Involving Smoothness and Tangent Spaces -- |g Lecture 18. |t Degree -- |g Lecture 19. |t Further Examples and Applications of Degree -- |g Lecture 20. |t Singular Points and Tangent Cones -- |g Lecture 21. |t Parameter Spaces and Moduli Spaces -- |g Lecture 22. |t Quadrics. |
| 520 | |a 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 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. | ||
| 588 | 0 | |a Print version record. | |
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| 830 | 0 | |a Graduate texts in mathematics ; |v 133. |0 http://id.loc.gov/authorities/names/n83723435. | |
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