Motivic distribution of rational curves
Event details
| Date | 16.05.2023 |
| Hour | 15:15 › 17:00 |
| Speaker | Loïs Faisant (Université Grenoble Alpes) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
In diophantine geometry, the Batyrev-Manin-Peyre conjecture originally concerns rational points on Fano varieties. It describes the asymptotic behaviour of the number of rational points of bounded height, when the bound becomes arbitrary large.
A geometric analogue of this conjecture deals with the asymptotic behaviour of the moduli space of rational curves on a complex Fano variety, when the « degree » of the curves « goes to infinity ». Various examples support the claim that, after renormalisation in a relevant ring of motivic integration, the class of this moduli space may converge to a constant which has an interpretation as a motivic Euler product.
In this talk, we will state this motivic version of the Batyrev-Manin-Peyre conjecture and give some examples for which it is known to hold : projective space, more generally toric varieties, and equivariant compactifications of vector spaces.
In a second part we will introduce the notion of equidistribution of curves and show that it opens a path to new types of results.
Practical information
- Informed public
- Free
Organizer
- Tanguy Vernet
Contact
- Monique Kiener (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)