Introduction to Plane Algebraic Curves

• Main Author: Kunz, Ernst (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2005.
• Subjects: Mathematics.; Algebraic geometry.; Associative rings.; Rings (Algebra).; Commutative algebra.; Commutative rings.; Algebra.; Field theory (Physics).; Applied mathematics.; Engineering mathematics.; Algebraic topology.; Algebraic Geometry.; Algebraic Topology.; Applications of Mathematics.; Commutative Rings and Algebras.; Associative Rings and Algebras.; Field Theory and Polynomials.

This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching t...

Table of Contents:

• Plane Algebraic Curves
• Ane Algebraic Curves
• Projective Algebraic Curves
• The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves
• Rational Functions on Algebraic Curves
• Intersection Multiplicity and Intersection Cycle of Two Curves
• Regular and Singular Points of Algebraic Curves. Tangents
• More on Intersection Theory. Applications
• Rational Maps. Parametric Representations of Curves
• Polars and Hessians of Algebraic Curves
• Elliptic Curves
• Residue Calculus
• Applications of Residue Theory to Curves
• The Riemann-Roch Theorem
• The Genus of an Algebraic Curve and of Its Function Field
• The Canonical Divisor Class
• The Branches of a Curve Singularity
• Conductor and Value Semigroup of a Curve Singularity.