Density of rational points on Del Pezzo surfaces of degree one
Event details
| Date | 18.10.2012 |
| Hour | 11:15 › 12:30 |
| Speaker | Ronald van Luijk (Leiden University) |
| Location |
AAC006
|
| Category | Conferences - Seminars |
We state conditions under which the set of rational points on a Del Pezzo surface of degree one over a global field is Zariski dense. For example, it suffices to require that the elliptic fibration induced by the anticanonical map has a nodal fiber over a rational point of the projective line. It also suffices to require the existence of a rational point that does not lie on six exceptional curves of the surface and that has order three on its fiber of the elliptic fibration. This allows us to show that within a parameter space for Del Pezzo surfaces of degree one over the real numbers, the set of those surfaces defined over the rational numbers for which
the set of rational points is Zariski dense, is dense with respect to the real analytic topology.
the set of rational points is Zariski dense, is dense with respect to the real analytic topology.
Practical information
- General public
- Free
Organizer
- Hélène Esnault (U. Duisburg-Essen),
Andrew Kresch (U. Zürich)
Bjorn Poonen (MIT)
Alexei Skorobogatov (Imperial College London).
Contact
- Rana Gherzeddine