Intersection Theory / by William Fulton.

Format:

Book

Author/Creator:

Fulton, William, 1939- Author.

Series:

Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 2.

Ergebnisse der Mathematik und ihrer Grenzgebiete, 0071-1136 ; Dritte Folge, volume 2

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebraic Geometry.

Local Subjects:

Algebraic Geometry.

Physical Description:

1 online resource (XIII, 470 p.)

Edition:

2nd ed. 1998.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1998.

Language Note:

English

Summary:

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.

Contents:

1. Rational Equivalence

2. Divisors

3. Vector Bundles and Chern Classes

4. Cones and Segre Classes

5. Deformation to the Normal Cone

6. Intersection Products

7. Intersection Multiplicities

8. Intersections on Non-singular Varieties

9. Excess and Residual Intersections

10. Families of Algebraic Cycles

11. Dynamic Intersections

12. Positivity

13. Rationality

14. Degeneracy Loci and Grassmannians

15. Riemann-Roch for Non-singular Varieties

16. Correspondences

17. Bivariant Intersection Theory

18. Riemann-Roch for Singular Varieties

19. Algebraic, Homological and Numerical Equivalence

20. Generalizations

Appendix A. Algebra

Appendix B. Algebraic Geometry (Glossary)

Notation.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9781461217008

1461217008