Workshop: Manin’s Conjecture for Del Pezzo Surfaces of Degree 5 with a Conic Fibration, Roger Heath-Brown

Speaker
Roger Heath-Brown, University of Oxford

Abstract
A DP5 with a conic fibration may be given in \(P^2 x P^1\) by the equation \begin{equation}y_1 Q_1(x_1,x_2,x_3) + y_2 Q_2(x_1,x_2,x_3) = 0,\end{equation}with quadratic forms \(Q_1, Q_2\) defined over the rationals. The talk will discuss the proof of Manin’s conjecture for such varieties in the generic case. This is joint work with Dan Loughran.