Iitaka fibrations and integral points: a family of arbitrarily polarized spherical threefolds

Studying Manin’s program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analogue of Iitaka fibrations, which have not yet been adequately formulated.