Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank
Event details
| Date | 29.09.2022 |
| Hour | 10:15 › 11:45 |
| Speaker | Julia Schneider (EPFL) |
| Location | |
| Category | Conferences - Seminars |
The Cremona group of rank N over a field K is the group of birational transformations of the projective N-space that are defined over K. In this talk, however, we will first focus on birational transformations of (non-trivial) Severi-Brauersurfaces, that is, surfaces that become isomorphic to the projective plane over the algebraic closure of K. In particular, we will prove that if such a surface contains a point of degree 6, then its group of birational transformations is not generated by elementsof finite order as it admits a surjective group homomorphism to the integers.
As an application, we use this result to study Mori fiber spaces over the field of complex numbers, for which the generic fiber is a non-trivial Severi-Brauer surface. Weprove that any group of cardinality at most the one of the complex numbers is a quotient of the Cremona group of rank 4 (and higher).
This is joint work in progress with Jérémy Blanc and Egor Yasinsky.
Practical information
- Informed public
- Free
Organizer
- Stefano Filipazzi
Contact
- Monique Kiener (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)