Description

Book Synopsis
The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. This book looks at the classic entry point to the subject: plane algebraic curves. It presents an introduction to algebraic geometry, which assumes the standard undergraduate mathematical topics.

Table of Contents
Introduction Affine algebraic curves and their equations The projective closure Tangents and singularities Polars and Hessian curves The dual curve and the Plucker formulas The ring of convergent power series Parametrizing the branches of a curve by Puiseux series Tangents and intersection multiplicities of germs of curves The Riemann surface of an algebraic curve The resultant Covering maps The implicit function theorem The Newton polygon A numerical invariant of singularities of curves Harnack's inequality Bibliography Subject index List of symbols.

Plane Algebraic Curves

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    A Paperback by American Mathem American Mathem

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      Book details

      Publisher American Mathematical Society
      Published 6/30/2001 12:00:00 AM
      ISBN-13 9780821821220
      978-0821821220
      ISBN-10 0821821229

      Description

      Book Synopsis
      The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. This book looks at the classic entry point to the subject: plane algebraic curves. It presents an introduction to algebraic geometry, which assumes the standard undergraduate mathematical topics.

      Table of Contents
      Introduction Affine algebraic curves and their equations The projective closure Tangents and singularities Polars and Hessian curves The dual curve and the Plucker formulas The ring of convergent power series Parametrizing the branches of a curve by Puiseux series Tangents and intersection multiplicities of germs of curves The Riemann surface of an algebraic curve The resultant Covering maps The implicit function theorem The Newton polygon A numerical invariant of singularities of curves Harnack's inequality Bibliography Subject index List of symbols.

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