Complex Algebraic Curves

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


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).


Riemann Surface Betti Number Algebraic Curve Algebraic Curf Real Projective Plane 
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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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