
Intersection Theory
William Fulton(Author)
Springer (Publisher)
2nd Edition
Published on 26. June 1998
Book
Paperback/Softback
XIII, 470 pages
978-0-387-98549-7 (ISBN)
Description
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.
Reviews / Votes
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 REVIEWSMore details
Edition
Second Edition 1998
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Edition type
New edition
Illustrations
XIII, 470 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 27 mm
Weight
733 gr
ISBN-13
978-0-387-98549-7 (9780387985497)
DOI
10.1007/978-1-4612-1700-8
Schweitzer Classification
Content
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.