# Seminar on toric varieties (Winter 24/25)

In this master seminar we will learn (some of) the theory of toric varieties, a class of varieties that can be described fairly explicitly in combinatorial terms, but that is large enough to contain many interesting examples and also often comes into play when studying general varieties or schemes.

The seminar will be carried out by Prof. Ulrich Görtz and Dr. Andreas Pieper. Talks can be given in English or German at the choice of the speaker.

If you are interested in participating in the seminar, please contact Andreas Pieper (`andreas.pieper@univ-rennes.fr`) as early as possible.

**Program:** pdf (in German; see below for a list of talks in English; we will be happy to provide more details on the talks in English, just get in touch)

**Schedule:** Tuesday 10-12am; first meeting: Oct. 8

**Prerequisites:** Algebraic Geometry 1 (basics of scheme theory); Algebraic Geometry 2 is useful, but not mandatory. If you know some “classical” algebraic geometry and attend the Algebraic Geometry 1 class in parallel, that could also work.

## Talks

1 | Introduction | N. N. |

2 | Convex polyhedral cones | N. N. |

3 | Affine toric varieties | N. N. |

4 | Fans and toric varieties | N. N. |

5 | Local properties of toric varieties | N. N. |

6 | Quotients of schemes by finite groups | N. N. |

7 | Toric surfaces, quotient singularities | N. N. |

8 | Proper toric varieties | N. N. |

9 | Blow-ups | N. N. |

10 | Smooth proper toric surfaces | N. N. |

11 | Resolution of singularities of toric varieties I | N. N. |

12 | Resolution of singularities of toric varieties II | N. N. |