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Introduction to algebraic geometry
Cutkosky, Steven Dale.
- ISBN:9781470435189
- Call Number : QA 564 .C8794 2018
- Main Entry: Cutkosky, Steven Dale.
- Title:Introduction to algebraic geometry / Steven Dale Cutkosky.
- Portion of title: Algebraic geometry
- Publisher:Providence, Rhode Island : AMS, 2018.
- Physical Description:xii, 484 p. ; 27 cm
- Series:Graduate studies in mathematics; v.188
- Notes:Includes bibliographical references and index
- Subject:Geometry, Algebraic.
Introduction to algebraic geometry
- Cover
- Title page
- Contents
- Preface
- Chapter 1. A Crash Course in Commutative Algebra
- Chapter 2. Affine Varieties
- Chapter 3. Projective Varieties
- Chapter 4. Regular and Rational Maps of Quasi-projective Varieties
- Chapter 5. Products
- Chapter 6. The Blow-up of an Ideal
- Chapter 7. Finite Maps of Quasi-projective Varieties
- Chapter 8. Dimension of Quasi-projective Algebraic Sets
- Chapter 9. Zariski’s Main Theorem
- Chapter 10. Nonsingularity
- Chapter 11. Sheaves
- Chapter 12. Applications to Regular and Rational Maps
- Chapter 13. Divisors
- 13.1. Divisors and the class group
- 13.2. The sheaf associated to a divisor
- 13.3. Divisors associated to forms
- 13.4. Calculation of some class groups
- 13.5. The class group of a curve
- 13.6. Divisors, rational maps, and linear systems
- 13.7. Criteria for closed embeddings
- 13.8. Invertible sheaves
- 13.9. Transition functions
- Chapter 14. Differential Forms and the Canonical Divisor
- Chapter 15. Schemes
- Chapter 16. The Degree of a Projective Variety
- Chapter 17. Cohomology
- Chapter 18. Curves
- Chapter 19. An Introduction to Intersection Theory
- Chapter 20. Surfaces
- Chapter 21. Ramification and Étale Maps
- 21.1. Norms and Traces
- 21.2. Integral extensions
- 21.3. Discriminants and ramification
- 21.4. Ramification of regular maps of varieties
- 21.5. Completion
- 21.6. Zariski’s main theorem and Zariski’s subspace theorem
- 21.7. Galois theory of varieties
- 21.8. Derivations and Kähler differentials redux
- 21.9. Étale maps and uniformizing parameters
- 21.10. Purity of the branch locus and the Abhyankar-Jung theorem
- 21.11. Galois theory of local rings
- 21.12. A proof of the Abhyankar-Jung theorem
- Chapter 22. Bertini’s Theorems and General Fibers of Maps
- Bibliography
- Index
- Back Cover