Softcover ISBN:  9780821807040 
Product Code:  CBMS/54 
List Price:  $32.00 
Individual Price:  $25.60 
Electronic ISBN:  9781470424169 
Product Code:  CBMS/54.E 
List Price:  $30.00 
Individual Price:  $24.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 54; 1984; 83 ppMSC: Primary 14; 13;
This book introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. It requires little technical background: much of the material is accessible to graduate students in mathematics. A broad survey, the book touches on many topics, most importantly introducing a powerful new approach developed by the author and R. MacPherson. It was written from the expository lectures delivered at the NSFsupported CBMS conference at George Mason University, held June 27–July 1, 1983.
The author describes the construction and computation of intersection products by means of the geometry of normal cones. In the case of properly intersecting varieties, this yields Samuel's intersection multiplicity; at the other extreme it gives the selfintersection formula in terms of a Chern class of the normal bundle; in general it produces the excess intersection formula of the author and R. MacPherson. Among the applications presented are formulas for degeneracy loci, residual intersections, and multiple point loci; dynamic interpretations of intersection products; Schubert calculus and solutions to enumerative geometry problems; RiemannRoch theorems.ReadershipGraduate students and research mathematicians interested in algebraic geometry.

Table of Contents

Chapters

Chapter 1. Intersections of Hypersurfaces

Chapter 2. Multiplicity and Normal Cones

Chapter 3. Divisors and Rational Equivalence

Chapter 4. Chern Classes and Segre Classes

Chapter 5. Gysin Maps and Intersection Rings

Chapter 6. Degeneracy Loci

Chapter 7. Refinements

Chapter 8. Positivity

Chapter 9. RiemannRoch

Chapter 10. Miscellany


Reviews

These notes have maintained their outstanding role as both a beautiful introduction and a masterly survey in this area of algebraic geometry. Now as before, W. Fulton's introductory notes are an excellent invitation to this subject, and a valuable spring of information for any mathematician interested in the methods of algebraic geometry in general.
Zentralblatt MATH


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 Book Details
 Table of Contents
 Reviews

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This book introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. It requires little technical background: much of the material is accessible to graduate students in mathematics. A broad survey, the book touches on many topics, most importantly introducing a powerful new approach developed by the author and R. MacPherson. It was written from the expository lectures delivered at the NSFsupported CBMS conference at George Mason University, held June 27–July 1, 1983.
The author describes the construction and computation of intersection products by means of the geometry of normal cones. In the case of properly intersecting varieties, this yields Samuel's intersection multiplicity; at the other extreme it gives the selfintersection formula in terms of a Chern class of the normal bundle; in general it produces the excess intersection formula of the author and R. MacPherson. Among the applications presented are formulas for degeneracy loci, residual intersections, and multiple point loci; dynamic interpretations of intersection products; Schubert calculus and solutions to enumerative geometry problems; RiemannRoch theorems.
Graduate students and research mathematicians interested in algebraic geometry.

Chapters

Chapter 1. Intersections of Hypersurfaces

Chapter 2. Multiplicity and Normal Cones

Chapter 3. Divisors and Rational Equivalence

Chapter 4. Chern Classes and Segre Classes

Chapter 5. Gysin Maps and Intersection Rings

Chapter 6. Degeneracy Loci

Chapter 7. Refinements

Chapter 8. Positivity

Chapter 9. RiemannRoch

Chapter 10. Miscellany

These notes have maintained their outstanding role as both a beautiful introduction and a masterly survey in this area of algebraic geometry. Now as before, W. Fulton's introductory notes are an excellent invitation to this subject, and a valuable spring of information for any mathematician interested in the methods of algebraic geometry in general.
Zentralblatt MATH