Introduction to Algebraic Geometry
eBook - PDF

Introduction to Algebraic Geometry

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Introduction to Algebraic Geometry

About this book

This book 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. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters.With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

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Yes, you can access Introduction to Algebraic Geometry by Steven Dale Cutkosky in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebraic Geometry. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title page
  3. Contents
  4. Preface
  5. Chapter 1. A Crash Course in Commutative Algebra
  6. Chapter 2. Affine Varieties
  7. Chapter 3. Projective Varieties
  8. Chapter 4. Regular and Rational Maps of Quasi-projective Varieties
  9. Chapter 5. Products
  10. Chapter 6. The Blow-up of an Ideal
  11. Chapter 7. Finite Maps of Quasi-projective Varieties
  12. Chapter 8. Dimension of Quasi-projective Algebraic Sets
  13. Chapter 9. Zariski’s Main Theorem
  14. Chapter 10. Nonsingularity
  15. Chapter 11. Sheaves
  16. Chapter 12. Applications to Regular and Rational Maps
  17. Chapter 13. Divisors
  18. Chapter 14. Differential Forms and the Canonical Divisor
  19. Chapter 15. Schemes
  20. Chapter 16. The Degree of a Projective Variety
  21. Chapter 17. Cohomology
  22. Chapter 18. Curves
  23. Chapter 19. An Introduction to Intersection Theory
  24. Chapter 20. Surfaces
  25. Chapter 21. Ramification and Étale Maps
  26. Chapter 22. Bertini’s Theorems and General Fibers of Maps
  27. Bibliography
  28. Index
  29. Back Cover