Integral points of bounded height via universal torsors
Event details
| Date | 28.11.2019 |
| Hour | 15:15 › 16:45 |
| Speaker | Florian Wilsch (IST Austria) |
| Location | |
| Category | Conferences - Seminars |
A conjecture of Manin’s relates the number of rational points of bounded height on Fano varieties with their geometric properties. Analogously to this conjecture on rational points, we study the distribution of integral points of bounded height. To do so, we parametrize integral points using universal torsors, and use analytic techniques to count integral points on the torsor – a method used previously to count rational points.
A result on a toric variety contradicts parts of a preprint by Chambert-Loir and Tschinkel. Morally, this is explained by an obstruction to the existence of integral points on a certain region of the variety that should have dominated the total number. We describe this obstruction and its relation with the geometric interpretation of asymptotic formulas for the number of integral points of bounded height.
A result on a toric variety contradicts parts of a preprint by Chambert-Loir and Tschinkel. Morally, this is explained by an obstruction to the existence of integral points on a certain region of the variety that should have dominated the total number. We describe this obstruction and its relation with the geometric interpretation of asymptotic formulas for the number of integral points of bounded height.
Practical information
- Informed public
- Free
Organizer
- Marta Pieropan
Contact
- Monique Kiener