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

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