Strictly nef divisors on singular threefolds

Abstract

Let X be a normal projective variety with klt singularities and L-X a strictly nef Q-divisor on X. In this paper, we study the singular version of Serrano's conjecture, i.e. the ampleness of K-X + tL(X) for t >> 1. We show that, if X is a Q-factorial Gorenstein terminal threefold, then K-X + tL(X) is ample for t >> 1 unless X is a weak Calabi-Yau variety (i.e. the canonical divisor K-X is a Q-torsion and the augmented irregularity q degrees(X) vanishes) with L-X center dot c(2)(X) = 0.