Introduction to Plane Algebraic Curves

• Κύριος συγγραφέας: Kunz, Ernst (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Birkhäuser Boston, 2005.
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.