Description
Book SynopsisThe 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 ContentsIntroduction 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.
