# Manchester Geometry Seminar 2006/2007

**5 October 2006. ** *Room M12,
Mathematics and Social Sciences building, Sackville Street. 4pm*
## The Rationality Problem and Birational Rigidity

Aleksandr Pukhlikov (University of Liverpool)

`pukh@liverpool.ac.uk`

The classical rationality problem investigates whether a given algebraic variety can be parametrised by rational functions. In other words, whether it is possible to introduce a global system of coordinates on a dense open subset. In this talk, we will show how the classical rationality problem in the higher-dimensional contexts generalizes to the problem of description of rationally connected structures on a given rationally connected fiber space. The key concept in higher-dimensional situation is that of birational rigidity. We will discuss some examples and open problems.