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Complex Algebraic Curves

Chapter
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Part of the UNITEXT book series (UNITEXT, volume 66)

Abstract

The equation f (x,y) = 0, where x and y are complex variables and f is a polynomial (with complex coefficients in general), defines a subset of the complex plane ℂ2 (with coordinates x and y) of dimension two, since the real dimension of a 2-dimensional complex plane is equal to 4, and equating to zero the complex number f (x,y) means equating to zero both its real part and its imaginary part; that is, we have two equations in the four real variables (Re x, Imx, Rey, Imy).

Keywords

Riemann Surface Betti Number Algebraic Curve Algebraic Curf Real Projective Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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