Ronan Terpereau

This talk is about a work in progress with Jeremy Blanc and Andrea Fanelli.

The so-called Cremona group is the group of birational transformations of the n-dimensional complex projective space. This group is not an algebraic group for n>1, but we can hope (at least in small dimension) classify its maximal connected algebraic subgroups. In dimension 2, the classification is old and quite easy (F. Enriques, 1893). In dimension 3, the first rigorous treatment was done by H. Umemura in the 1980’s in a series of five (quite long and technical) papers. In this talk I will explain how we can hope to recover his results in a much simpler way using the now well-developed Mori theory and discuss several possible generalizations.