New Preprint

December 2019

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

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.

Birational Geometry, Kahler-Einstein Metrics, and Degenerations

November 2019, Pohang

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

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.