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
Note that ex-directory lists are not shown. |
## Other listsBiocomputing Workshops Cambridge Area Sequencing Informatics Meeting VII (2015) Philosophy of Education Society of Great Britain: Cambridge Branch## Other talksTBA South Africa 2014 TBC Spectacular Chemistry Demonstration Lecture Bypassing the brave new world: reporting transgenic mice in the early 1980s Thermostabilisation of G protein-coupled receptors to facilitate structure determination |