Florin Ambro
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We discuss the classification of germs of toric Fano fibrations, extending work of A. Borisov in the case of Q-factorial toric singularities. As an application, we verify in the toric case a conjecture of V. Shokurov on the existence of complements with bounded index and prescribed singularities.