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Intersection Theory

  • Book
  • © 1984

Overview

Authors:
  1. William Fulton

    1. Department of Mathematics, Brown University, Providence, USA

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Table of contents (21 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  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
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Keywords

About this book

From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen­ turies, intersection theory has played a central role. Since its role in founda­ tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his­ tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel­ op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen­ dices. Some of the examples, and a few of the later sections, require more spe­ cialized knowledge. The text is designed so that one who understands the con­ structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa­ cilitate use as a reference.

Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    William Fulton

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