Presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized.
Presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized.
Steven Dale Cutkosky, University of Missouri, Columbia, MO.
Inhaltsangabe
1. A crash course in commutative algebra 2. Affine varieties 3. Projective varieties 4. Regular and rational maps of quasi-projective varieties 5. Products 6. The blow-up of an ideal 7. Finite maps of quasi-projective varieties 8. Dimension of quasi-projective algebraic sets 9. Zariski's main theorem 10. Nonsingularity 11. Sheaves 12. Applications to regular and rational maps 13. Divisors 14. Differential forms and the canonical divisor 15. Schemes 16. The degree of a projective variety 17. Cohomology 18. Curves 19. An introduction to intersection theory 20. Surfaces 21. Ramification and etale maps 22. Bertini's theorem and general fibers of maps 23. Bibliography 24. Index.
1. A crash course in commutative algebra 2. Affine varieties 3. Projective varieties 4. Regular and rational maps of quasi-projective varieties 5. Products 6. The blow-up of an ideal 7. Finite maps of quasi-projective varieties 8. Dimension of quasi-projective algebraic sets 9. Zariski's main theorem 10. Nonsingularity 11. Sheaves 12. Applications to regular and rational maps 13. Divisors 14. Differential forms and the canonical divisor 15. Schemes 16. The degree of a projective variety 17. Cohomology 18. Curves 19. An introduction to intersection theory 20. Surfaces 21. Ramification and etale maps 22. Bertini's theorem and general fibers of maps 23. Bibliography 24. Index.
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