Introduction to Plane Algebraic Curves

Häftad, Engelska, 2005

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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 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.

Produktinformation

Utgivningsdatum2005-08-15
Mått155 x 235 x 14 mm
Vikt445 g
FormatHäftad
SpråkEngelska
Antal sidor294
Upplaga2005
FörlagBirkhauser Boston
ISBN9780817643812
ÖversättareBelshoff, Richard G., Belshoff, Richard G

Tillhör följande kategorier

Tillämpad matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

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.

"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