Density of rational points on Del Pezzo surfaces of degree one.

Density of rational points on Del Pezzo surfaces of degree one.

Abstract: 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. 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. This is joint work with Cecilia Salgado.