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Plane Algebraic Curves

About this Title

Gerd Fischer, Heinrich-Heine-Universität, Düsseldorf, Germany. Translated by Leslie Kay

Publication: The Student Mathematical Library
Publication Year 2001: Volume 15
ISBNs: 978-0-8218-2122-0 (print); 978-1-4704-2131-1 (online)
DOI: http://dx.doi.org/10.1090/stml/015
MathSciNet review: MR1836037
MSC: Primary 14H50; Secondary 14-01, 14N05, 32B10, 51N35

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Table of Contents

Front/Back Matter

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Chapters

• Chapter 0. Introduction
• Chapter 1. Affine algebraic curves and their equations
• Chapter 2. The projective closure
• Chapter 3. Tangents and singularities
• Chapter 4. Polars and Hessian curves
• Chapter 5. The dual curve and the Plücker formulas
• Chapter 6. The ring of convergent power series
• Chapter 7. Parametrizing the branches of a curve by Puiseux series
• Chapter 8. Tangents and intersection multiplicities of germs of curves
• Chapter 9. The Riemann surface of an algebraic curve
• Appendix 1. The resultant
• Appendix 2. Covering maps
• Appendix 3. The implicit function theorem
• Appendix 4. The Newton polygon
• Appendix 5. A numerical invariant of singularities of curves
• Appendix 6. Harnack’s inequality

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