Number Theory Seminar: Rosa Winter (UniDistance Suisse)

Title: Many rational points on del Pezzo surfaces of low degree

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 $d\geq3$, these are the smooth surfaces of degree $d$ in $\mathbb{P}^d$). 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 \textsl{Hilbert property} for del Pezzo surfaces of degree 1.

Spiegelgasse 5, Seminarraum 05.002

Export event as iCal