Fernando Figueroa Zamora (Princeton)

Tuesday, October 18, 2022 - 1:45pm

PDL C-38

**Pre seminar 1:45-2:30**

**Title:**Coregularity and Complements of Fano Varieties.

**Abstract:**In this pre-talk we will define the coregularity and complements of Fano pairs. We will see some of their basic properties and some examples.

**Seminar 2:30-3:20**

**Title**: Bounded Complements for Fano varieties of coregularity one

**Abstract:**

The coregularity of a Fano variety is an invariant that is always smaller than the dimension. One of the qualities of the coregularity is that certain bounds depending on the dimension extend to bounds depending on the coregularity, hence giving us sharper bounds for high dimension and low coregulairty varieties. By the work of Birkar one can bound the complements of Fano varieties in terms of their dimension. In this talk we will bound the complements of Fano varieties of coregularity one. We also will give a proof of this result for any coregularity under the assumption of the boundedness of the index and b-representation of Calabi-Yau pairs of fixed dimension. This is joint work with Stefano Filipazzi, Joaquín Moraga and Junyao Peng.