December 2019

Stability of fibrations over one-dimensional bases
with H. Ahmadinezhad and M. Fedorchuk

Abstract:
A Mori fiber space is called birationally rigid if, roughly speaking, it has only one Mori fiber space structure. I will talk about birational rigidity of singular del Pezzo fibrations. I will explain the essence of the method of proving birational rigidity: Noether-Fano method, also known as method of maximal singularities. I will discuss the differences in applying this to Fano varieties and Mori fiber spaces with a positive dimensional base.

November 2019

Title:On embeddings of Klein simple group into the Cremona group.

Abstract:
The Cremona group is the group of the birational transformations of the projective space. It is known that for any finite subgroup G in the Cremona group there is a rational variety X on each G acts biregularly. By running G-MMP on X we get a rational GQ-Mori fiber space. The study of embeddings of G into the Cremona group is equivalent to study of rational GQ-Mori fiber spaces. I will talk about PSL_2(7)Q-del Pezzo fibrations, their rationality, and the relation to quotients of certain quartic threefolds.
This a joint work with Takuzo Okada. This talk is related to his talk at this conference.