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Introduction to Plane Algebraic Curves by Ernst Kunz (2005, Perfect)
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Format: Paperback or Softback. Your Privacy. ISBN: 9780817643812. Condition Guide. Publication Date: 8/15/2005. Item Availability.
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About this product
Product Identifiers
PublisherBirkhäuser Boston
ISBN-100817643818
ISBN-139780817643812
eBay Product ID (ePID)45394688
Product Key Features
Number of PagesXiv, 294 Pages
Publication NameIntroduction to Plane Algebraic Curves
LanguageEnglish
Publication Year2005
SubjectTopology, Geometry / Algebraic, Applied
TypeTextbook
Subject AreaMathematics
AuthorErnst Kunz
FormatPerfect
Dimensions
Item Height0.2 in
Item Weight34.2 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2005-048053
Dewey Edition22
Reviews"This text stands out by the author's...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 Reviews 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, "This text stands out by the author's...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 Reviews 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, From a review of the German edition: "YT'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 studentsThe whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivationhighly enlightening, motivating and entertaining at the same timeOne simply cannot do better in writing such a textbook."Zentralblatt MATH, "This text stands out by the author's...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
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.3/52
Table Of ContentPlane 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.
SynopsisThis 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. Kunz's 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., 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 di'erent from, for instance, the book of Brieskorn-Kn¨ orrer [BK], where the geometric-topological-analytic aspects are particularly stressed, and where there is more emphasis on the history of the subject. Since these things are explained there in great detail, and with manybeautiful pictures,Ifeltrelievedoftheobligationtogointothetopol- icalandanalyticalconnections. Inthe lectures Irecommendedto the students that they read the appropriate sections of Brieskorn-Kn¨ orrer[BK]. The book by G. Fischer [F] can also serve this purpose. We will study algebraic curves over an algebraically closed ?eldK., * 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
LC Classification NumberQA564-609
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