|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 listsCambridge RNA Club Sir Andrew Motion Visits Cambridge in War Poets Event Professor Chris Bishop
Other talks"Payment is applause: markets and business models past, present and future" HONORARY FELLOWS LECTURE - Molecules against cancer or for very long term memory Methodologies for the functional annotation of GWAS loci: Examples from the 5p12 breast cancer susceptibility locus TBC (single-cell sequencing/transcriptomics) Butterfly Genetics Spectacular Chemistry Demonstration Lecture