Bounding non-rationality of divisors on 3-fold Fano fibrations.

In this paper we investigate non-rationality of divisors on 3-fold log Fano fibrations (X , B) → Z under mild conditions. We show that if D is a component of B with coefficient ≥ t > 0 which is contracted to a point on Z, then D is birational to ℙ¹ × C, where C is a smooth projective curve with gonality bounded depending only on t. Moreover, if t > 1/2, then genus of C is bounded depending only on t. [ABSTRACT FROM AUTHOR]