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Working paper

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

Loginov K., Birkar C.
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 ℙ^1×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.