Strictly nef divisors on singular threefolds

Abstract

Let X be a normal projective threefold with mild singularities, and L X a strictly nef Q-divisor on X. We first show the ampleness of K X + tL X with sufficiently large t if either the Kodaira dimension κ(X) = 0 or the augmented irregularity q • (X) = 0. Second, we study the rational connectedness of a projective klt pair (X, ∆) with the anti-log canonical divisor −(K X + ∆) being strictly nef.