Algebraic curves are irreducible (affine or projective) 1-dimensional schemes over a field k. We study their (non-)singularity by easier alternative criteria, leading to a process of desingularization called normalization. Regular projective curves are equivalently classified by their function fields. Further topics are morphisms between such curves and their ramification, divisors, differential forms and the Theorem of Riemann- Roch.

Kurs im HIS-LSF