Introduction to Plane Algebraic Curves
Birkhauser Boston Inc (Verlag)
978-0-8176-4381-2 (ISBN)
* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook
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.
| Übersetzer | Richard G. Belshoff |
|---|---|
| Zusatzinfo | 52 Illustrations, black and white; XIV, 294 p. 52 illus. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8176-4381-8 / 0817643818 |
| ISBN-13 | 978-0-8176-4381-2 / 9780817643812 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
