Plane algebraic curves
This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.
Read More ↓Title Statements
- Full title :Plane algebraic curves / Gerd Fischer ; translated by Leslie Kay.
Summary
This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.
Read More ↓Edition Statements
- Publication Date:June 2001.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence
- Language:eng
- Publication Date:June 2001.
The Physical Object
- Description:1 online resource.
Edition Identifiers
- ISBN:9781470421311, 1470421313, 0821821229, 9780821821220
- oclc:ocn907372188
- LC Classification:QA567
- Dewey Decimal:516.3/52
Table of Contents
Cover; Title; Copyright; Contents; Preface to the English Edition; Preface to the German Edition; Chapter 0. Introduction; 0.1. Lines; 0.2. Circles; 0.3. The Cuspidal Cubic; 0.4. The Nodal Cubic; 0.5. The Folium of Descartes; 0.6. Cycloids; 0.7. Klein Quartics; 0.8. Continuous Curves; Chapter 1. Affine Algebraic Curves and Their Equations; 1.1. The Variety of an Equation; 1.2. Affine Algebraic Curves; 1.3. Study's Lemma; 1.4. Decomposition into Components; 1.5. Irreducibility and Connectedness; 1.6. The Minimal Polynomial; 1.7. The Degree; 1.8. Points of Intersection with a Line.
Chapter 2. The Projective Closure2.1. Points at Infinity; 2.2. The Projective Plane; 2.3. The Projective Closure of a Curve; 2.4. Decomposition into Components; 2.5. Intersection Multiplicity of Curves and Lines; 2.6. Intersection of Two Curves; 2.7. Bézout's Theorem; Chapter 3. Tangents and Singularities; 3.1. Smooth Points; 3.2. The Singular Locus; 3.3. Local Order; 3.4. Tangents at Singular Points; 3.5. Order and Intersection Multiplicity; 3.6. Euler's Formula; 3.7. Curves through Prescribed Points; 3.8. Number of Singularities; 3.9. Chebyshev Curves; Chapter 4. Polars and Hessian Curves.
4.1. Polar…
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