Algebraic geometry : a first course

By: Harris JoeMaterial type: TextTextSeries: Graduate Texts in Mathematics ; Vol. 133Publication details: New York: Springer-Verlag, [c1992]Description: 328 pISBN: 9780387977164Subject(s): MathematicsLOC classification: QA564Online resources: Click here to access online
Contents:
Part 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 Part 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
Summary: This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners. --- summary provided by publisher
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Mathematic Rack No 6 QA564 (Browse shelf (Opens below)) Available Billno: 42878 ; Billdate: 19.03.2019 01830
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Part 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

Part 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

This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners. --- summary provided by publisher

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