**Credits** |
8 credit points |

**Instructors** |
Geer, G.B.M. van der (Universiteit van Amsterdam) |

**E-mail** |
geer@science.uva.nl |

**Prerequisites** |
A healty knowlegde of complex function theory. |

**Description** |
This course gives an introduction to the theory of Riemann surfaces and algebraic curves. After treating sheaves and their cohomology, differential forms and residues we intend to prove the theorem of Riemann-Roch and Serre-duality. After that we discuss coverings of Riemann surfaces, the Hurwitz-Zeuthen formula and hyperelliptic Riemann surfaces. Finally, we shall treat Jacobian varieties the Abel-Jacobi map and we end with algebraic curves. |

**Organization** |
Besides attending the lectures students are supposed to work on exercises. |

**Examination** |
Examination is either oral or written. Also a project is possible. |

**Literature** |
O. Forster: Lectures on Riemann surfaces. Graduate Texts in Mathematics, 81. Springer-Verlag, New York-Berlin. Further literature will be given during the course. |