Manin's conjecture for certain spherical threefolds
We study rational points on two families of hypersurfaces in toric
varieties which are spherical threefolds when equipped with a suitable
action of the reductive group SL_2 x G_m. We are interested in the
asymptotic behavior of the number of rational points of bounded height,
which is predicted by a conjecture of Manin, refined by Batyrev,
Tschinkel, and Peyre. This is joint work with Ulrich Derenthal.