“Many rational points on del Pezzo surfaces of low degree”
Martedì 10 Marzo 2026, ore 14:30 - Aula 2AB40 - Rosa Winter (Albert-Ludwigs-Universität Freiburg)
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 less is known about the set of rational points on the surface. I will give an overview of different notions of “many” rational points, go over several results for rational points on del Pezzo surfaces of degree 1 and 2, and show how these relate to some of the major open questions on the arithmetic of surfaces.
