Abstract
In this paper we investigate singularities on toric fibrations. In this context we study a conjecture of Shokurov (a special case of which is due to MKernan which roughly says that if is an -lc Fano-type log Calabi-Yau fibration, then the singularities of the log base are bounded in terms of and where and are the discriminant and moduli divisors of the canonical bundle formula. A corollary of our main result says that if is a toric Fano fibration with being -lc, then the multiplicities of the fibres over codimension one points are bounded depending only on and . Bibliography: 20 titles.
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