Seminar room: 05.002

## Seminar Algebra and Geometry: Yuri Prokhorov (Steklov Mathematical Institute, Moscow)

**Birational transformations of tetragonal conic bundles**

A conic bundle f: X\to S is a flat morphism of smooth varieties whose fibers are plane conics.

In this talk, I will first discuss application of Sarkisov program to the rationality problem of algebraic varieties having conic bundle structures.

Then I concentrate on some special, so-called * **tetragonal* types of conic bundles, which lie on the "boundary" between birationally rigid and non-rigid ones and are especially interesting for this reason.

The second part of the talk is based on the joint work in progress with V. Shokurov.

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