Intersection Theory

1. Front Matter

   Pages I-XIII

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2. Introduction

   • William Fulton

   Pages 1-5

3. Rational Equivalence

   • William Fulton

   Pages 6-27

4. Divisors

   • William Fulton

   Pages 28-46

5. Vector Bundles and Chern Classes

   • William Fulton

   Pages 47-69

6. Cones and Segre Classes

   • William Fulton

   Pages 70-85

7. Deformation to the Normal Cone

   • William Fulton

   Pages 86-91

8. Intersection Products

   • William Fulton

   Pages 92-118

9. Intersection Multiplicities

   • William Fulton

   Pages 119-129

10. Intersections on Non-singular Varieties

    • William Fulton

    Pages 130-152

11. Excess and Residual Intersections

    • William Fulton

    Pages 153-174

12. Families of Algebraic Cycles

    • William Fulton

    Pages 175-194

13. Dynamic Intersections

    • William Fulton

    Pages 195-209

14. Positivity

    • William Fulton

    Pages 210-234

15. Rationality

    • William Fulton

    Pages 235-241

16. Degeneracy Loci and Grassmannians

    • William Fulton

    Pages 242-279

17. Riemann-Roch for Non-singular Varieties

    • William Fulton

    Pages 280-304

18. Correspondences

    • William Fulton

    Pages 305-318

19. Bivariant Intersection Theory

    • William Fulton

    Pages 319-338

20. Riemann-Roch for Singular Varieties

    • William Fulton

    Pages 339-369

From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the foundations of this theory, and to indicate the range of classical and modern applications. Although a comprehensive history of this vast subject is not attempted, the author points out some of the striking early appearances of the ideas of intersection theory. A suggested prerequisite for the reading of this book is a first course in algebraic geometry. Fulton's introduction to intersection theory has been well used for more than 10 years. It is still the only existing complete modern treatise of the subject and received the Steele Prize for best exposition in August 1996.

• Chern class
• Division
• Divisor
• Equivalence
• algebra
• algebraic geometry
• eXist
• equation
• form
• geometry
• history of mathematics
• story
• vector bundle

Review of 1st Edition "...This text, with its brilliant content and excellently arranged, is a prime mover in algebraic geometry, and a must for each algebraic geometer! It is an indispensable reference book, an outstanding textbook, and a great source for geometric research in the future." -- MATHEMATICAL REVIEWS

• Department of Mathematics, University of Michigan, Ann Arbor, USA

  William Fulton

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