Density of rational points on a family of del Pezzo surfaces of degree 1 – Rosa Winter
Rosa Winter
Max Planck Institute for Mathematics in the Sciences à Leipzig
https://personal-homepages.mis.mpg.de/winter/
Date(s) : 17/12/2020 iCal
11h00 - 12h00
Del Pezzo surfaces are classified by their degree d, which is an integer between 1 and 9 (for d ≥ 3, these are the smooth surfaces of degree d in ℙ^d). For del Pezzo surfaces of degree at least 2 over a field k, we know that the set of k-rational points is Zariski dense provided that the surface has one k-rational point to start with (that lies outside a specific subset of the surface for degree 2). However, for del Pezzo surfaces of degree 1 over a field k, even though we know that they always contain at least one k-rational point, we do not know if the set of k-rational points is Zariski dense in general. I will talk about a result that is joint work with Julie Desjardins, in which we give necessary and sufficient conditions for the set of k-rational points on a specific family of del Pezzo surfaces of degree 1 to be Zariski dense, where k is a number field. I will compare this to previous results.
Meeting ID : 921 9584 8065
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