Let O(D) and O(D’) be an ample and a nef line bundle on a smooth toric variety X, respectively. Oda asked, whether the multiplication map of global sections to sections of O(D+D’) is onto. Annoyingly, this question remains unsolved to this day.

Gubeladze developed a novel convex geometric tool in order to show surjectivity in the case both D and D’ are multiples of the same sufficiently ample divisor. In joint work with Jan Hofmann, we extend Gubeladze’s notion to the general ample+nef case and prove surjectivity if D is really, really ample compared to D’. What we actually do is to add lattice points in lattice polytopes.