A pre-introduction to algebraic geometry by pictures

Donu Arapura

A complex algebraic plane curve is the set of complex solutions to a polynomial equation f(x, y)=0. This is a 1 complex dimensional subset of C2, or in more conventional terms it is a surface living in a space of 4 real dimensions. These objects are also called Riemann surfaces, at least away from the singularities. The study of these objects and their generalizations within algebraic geometry involves a lot of technical material, and it is easy to forget that this is geometry. So I've put together a small picture gallery, with just enough theory to explain them. More systematic treatments can be found in the references given below.



  1. F. Kirwan, Complex algebraic curves
  2. R. Miranda, Algebraic curves and Riemann surfaces
  3. M. Reid, Undergraduate algebraic geometry
  4. G. Springer, Riemann surfaces
More information about algebraic geometry can be found here. Information about how this document was produced can be found here.