|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Density of rational points on Del Pezzo surfaces of degree one
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:
Note that ex-directory lists are not shown.
Other listsBeyond Profit Think Tank Cambridge Science Festival Past PhD Symposium 5 January 2015
Other talksAn equivalent barotropic view of the Southern Ocean and Antarctic Circumpolar Current Geodynamics and Two-Phase Flow: A Computational Perspective The 'Primary Chronicle' and the Origin of the Kyivan Rus' State Cracking the Nut: The Psychology of Food Choice C++, the Standard Library, and overloading Economic and welfare effects of UK energy tax reform