Rosa Winter:
Many rational points on del Pezzo surfaces of low degree
Time and place
Friday, 17.10.25, 10:30-11:30, Seminarraum 404
Abstract
Let X be an algebraic variety over a number field k. In arithmetic geometry we are interested in the set X(k) of k-rational points on X. Questions one might ask are, is X(k) empty or not? And if it is not empty, how ‘large’ is X(k)? Del Pezzo surfaces are surfaces classified by their degree d, which is an integer between 1 and 9 (for d at least 3, these are the smooth surfaces of degree d in P^d). The lower the degree, the more complex del Pezzo surfaces are. I will give an overview of different notions of ‘many’ rational points, and go over several results for rational points on del Pezzo surfaces of degree 1 and 2. I will then focus on work in progress joint with Julian Demeio and Sam Streeter on the so-called Hilbert property for del Pezzo surfaces of degree 1.