Plane Algebraic Curves

Frontcover
American Mathematical Soc., 2001 - 231 Seiten
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The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. In this book, Fischer looks at the classic entry point to the subject: plane algebraic curves. Here one quickly sees the mix of algebra and geometry, as well as analysis and topology, that is typical of complex algebraic geometry, but without the need for advanced techniques from commutative algebra or the abstract machinery of sheaves and schemes.
  

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Inhalt

Introduction
1
Affine Algebraic Curves and Their Equations
13
The Projective Closure
23
Tangents and Singularities
35
Polars and Hessian Curves
59
The Dual Curve and the Plücker Formulas
73
The Ring of Convergent Power Series
95
Parametrizing the Branches of a Curve by Puiseux Series
125
Tangents and Intersection Multiplicities of Germs of Curves
147
The Riemann Surface of an Algebraic Curve
163
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Elementary Algebraic Geometry
Klaus Hulek
Eingeschränkte Leseprobe - 2003
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