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Publication# The Nonvanishing Problem for varieties with nef anticanonical bundle

Abstract

We prove that if (X, A) is a threefold pair with mild singularities such that -(KX + A) is nef, then the numerical class of -(KX + A) is effective.

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In mathematics, the canonical bundle of a non-singular algebraic variety of dimension over a field is the line bundle , which is the nth exterior power of the cotangent bundle on . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle . Equivalently, it is the line bundle of holomorphic n-forms on . This is the dualising object for Serre duality on . It may equally well be considered as an invertible sheaf.

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