Strictly nef divisors on singular threefolds

Abstract

Let [Formula: see text] be a normal projective variety with klt singularities and [Formula: see text] a strictly nef [Formula: see text]-divisor on [Formula: see text]. In this paper, we study the singular version of Serrano’s conjecture, i.e. the ampleness of [Formula: see text] for [Formula: see text]. We show that, if [Formula: see text] is a [Formula: see text]-factorial Gorenstein terminal threefold, then [Formula: see text] is ample for [Formula: see text] unless [Formula: see text] is a weak Calabi–Yau variety (i.e. the canonical divisor [Formula: see text] is a [Formula: see text]-torsion and the augmented irregularity [Formula: see text] vanishes) with [Formula: see text].