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Introduction to Plane Algebraic Curves

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Cover of 'Introduction to Plane Algebraic Curves'

Table of Contents

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    Book Overview
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    Chapter 1 Ane Algebraic Curves
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    Chapter 2 Projective Algebraic Curves
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    Chapter 3 The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves
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    Chapter 4 Rational Functions on Algebraic Curves
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    Chapter 5 Intersection Multiplicity and Intersection Cycle of Two Curves
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    Chapter 6 Regular and Singular Points of Algebraic Curves. Tangents
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    Chapter 7 More on Intersection Theory. Applications
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    Chapter 8 Rational Maps. Parametric Representations of Curves
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    Chapter 9 Polars and Hessians of Algebraic Curves
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    Chapter 10 Elliptic Curves
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    Chapter 11 Residue Calculus
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    Chapter 12 Applications of Residue Theory to Curves
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    Chapter 13 The Riemann-Roch Theorem
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    Chapter 14 The Genus of an Algebraic Curve and of Its Function Field
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    Chapter 15 The Canonical Divisor Class
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    Chapter 16 The Branches of a Curve Singularity
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    Chapter 17 Conductor and Value Semigroup of a Curve Singularity
Attention for Chapter 3: The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves
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