# Intersection Theory

• William Fulton
Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 2)

1. Front Matter
Pages I-XI
2. William Fulton
Pages 1-5
3. William Fulton
Pages 6-27
4. William Fulton
Pages 28-46
5. William Fulton
Pages 47-69
6. William Fulton
Pages 70-85
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Pages 86-91
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Pages 92-118
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Pages 119-129
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Pages 130-152
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Pages 153-174
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Pages 175-194
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Pages 210-234
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20. William Fulton
Pages 339-369
21. William Fulton
Pages 370-392
22. William Fulton
Pages 393-405
23. Back Matter
Pages 406-472

### Introduction

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.

### Keywords

Algebraische Geometrie Blowing up Divisor Schnittheorie Topologie Zahlentheorie algebra algebraic geometry boundary element method design equation geometry number theory theorem toplogy

#### Authors and affiliations

• William Fulton
• 1
1. 1.Department of MathematicsBrown UniversityProvidenceUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-662-02421-8
• Copyright Information Springer-Verlag Berlin Heidelberg 1984
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-662-02423-2
• Online ISBN 978-3-662-02421-8
• Series Print ISSN 0071-1136
• Buy this book on publisher's site