## 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 C^{2}, 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.

#### Gallery

#### References

- F. Kirwan, Complex algebraic curves
- R. Miranda, Algebraic curves and Riemann surfaces
- M. Reid, Undergraduate algebraic geometry
- G. Springer, Riemann surfaces

More information about algebraic geometry can be found here.
Information about how this document was produced can be
found
here.