COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Density of rational points on Del Pezzo surfaces of degree one

## Density of rational points on Del Pezzo surfaces of degree oneAdd to your list(s) Download to your calendar using vCal - Ronald van Luijk (Leiden)
- Wednesday 13 February 2013, 14:15-15:15
- MR 13, CMS.
If you have a question about this talk, please contact Caucher Birkar. We state conditions under which the set of rational points on a Del Pezzo surface of degree one over an infinite 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. We also state conditions that may be satisfied for every del Pezzo surface and that can be verified with a finite computation for any del Pezzo surface that does satisfy them. This is joint work with Cecilia Salgado. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- MR 13, CMS
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsType the title of a new list here Early Modern Economic and Social History Seminars Centre of African Studies Occasional Talks## Other talksWhy does cardiac function deteriorate in heart failure and how does phosphodiesterase 5 inhibition help? Imaging techniques and novel tools for early detection and intervention The cardinal points and the structure of geographical knowledge in the early twelfth century Emissions and Chemistry of air pollution in London and Beijing: a tale of two cities. Constructing the organism in the age of abstraction |