# 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, S-U-3.02

**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 | Andreas Pieper |

2 | Convex polyhedral cones | Adam Madro |

3 | Affine toric varieties | Irene Pivari |

4 | Fans and toric varieties | Yikun Fan |

5 | Local properties of toric varieties | Francesco Barban |

6 | Quotients of schemes by finite groups | Jacopo Ravera |

7 | Toric surfaces, quotient singularities | Irene Pivari |

7 1/2 | Projective toric varieties | Adam Madro |

8 | Proper toric varieties | Leyan Chen |

9 | Blow-ups | Jacopo Ravera |

10 | Smooth proper toric surfaces | Yikun Fan |

11 | Resolution of singularities of toric varieties I | Sanskar Agrawal |

12 | Resolution of singularities of toric varieties II | Francesco Barban |

13 | Orbits of the torus action | Sanskar Agrawal |

14 | Divisors on toric varieties | Leyan Chen |