Introduction to Plane Algebraic Curves by Ernst Kunz (English) Paperback Book

Description: Introduction to Plane Algebraic Curves by Ernst Kunz, Richard G. Belshoff Treats an introduction to commutative ring theory and algebraic plane curves, with the algebraic facts. This book on plane algebraic curves presents Kunzs conception of teaching topics in commutative algebra together with their applications to algebraic geometry. It includes examples, exercises, figures, and suggestions for further study. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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.Kunzs proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook. Notes This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the reader only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunzs proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. Examples, exercises, figures, and suggestions for further study round out this fairly self-contained textbook. Back Cover 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. Kunzs proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Most important to this text: * Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves * Presents residue theory in the affine plane and its applications to intersection theory * Methods of proof for the Riemann-Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook From a review of the German edition: "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students... The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation...highly enlightening, motivating and entertaining at the same time... One simply cannot do better in writing such a textbook." --Zentralblatt MATH 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. Review "This text stands out by the authors...writing style characterized by its systematic representations, didactical perfection, comprehensiveness, mathematical rigor, thematic determination, and striving for self-containedness. Like in most of his other textbooks on algebra and algebraic geometry [the author] focuses on the inseparable interplay between those two branches of mathematics, and again he presents and hits for further reading. There is no doubt that the international mathematical community, including students and teachers, will welcome the overdue English edition of this masterly textbook as a very special and useful addition to the great standard texts on plane curves." —Zentralblatt MATH"The translation of the book is impeccable, one would never imagine that the book was written in another language. Moreover, the exposition is very clear and the reading flows nicely. The book is a very good choice for a first course in algebraic geometry. As a prerequisite the reader needs some basic notions of algebra; the rest of the needed algebraic requirements are developed in the appendices." —MAA ReviewsFrom a review of the German edition: "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students…The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation…highly enlightening, motivating and entertaining at the same time…One simply cannot do better in writing such a textbook." —Zentralblatt MATH Long Description This book is a slightly extended elaboration of a course on commutative ring theory and plane algebraic curves that I gave several times at the Univ- sity of Regensburg to students with a basic knowledge of algebra. I thank Richard Belsho? for translating the German lecture notes into English and for preparing the numerous ?gures of the present text. As in my bookIntroduction to Commutative Algebra and Algebraic Ge- etry, this book follows the philosophy that the best way to introduce com- tative algebra is to simultaneously present applications in algebraicgeometry. This occurs here on a substantially more elementary level than in my earlier book, for we never leave plane geometry, except in occasional notes without proof, as for instance that the abstract Riemann surface of a plane curve is "actually" a smooth curve in a higher-dimensional space. In contrast to other presentations of curve theory, here the algebraic viewpoint stays strongly in the foreground. This is completely dierent from, for instance, the book of Brieskorn-Kn Review Quote "This text stands out by the authors...writing style characterized by its systematic representations, didactical perfection, comprehensiveness, mathematical rigor, thematic determination, and striving for self-containedness. Like in most of his other textbooks on algebra and algebraic geometry [the author] focuses on the inseparable interplay between those two branches of mathematics, and again he presents and hits for further reading. There is no doubt that the international mathematical community, including students and teachers, will welcome the overdue English edition of this masterly textbook as a very special and useful addition to the great standard texts on plane curves." Feature 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 Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook Description for Sales People This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the reader only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunzs proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. Examples, exercises, figures, and suggestions for further study round out this fairly self-contained textbook. Details ISBN0817643818 Author Richard G. Belshoff Short Title INTRO TO PLANE ALGEBRAIC CURVE Language English Translator Richard G. Belshoff ISBN-10 0817643818 ISBN-13 9780817643812 Media Book Format Paperback DEWEY 516.352 Year 2005 Birth 1933 Imprint Birkhauser Boston Inc Place of Publication Secaucus Country of Publication United States DOI 10.1007/b99066;10.1007/0-8176-4443-1 AU Release Date 2005-08-15 NZ Release Date 2005-08-15 US Release Date 2005-08-15 UK Release Date 2005-08-15 Pages 294 Publisher Birkhauser Boston Inc Edition Description 2005 ed. Edition 2005th Publication Date 2005-08-15 Illustrations 52 Illustrations, black and white; XIV, 294 p. 52 illus. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. 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