The Nonvanishing problem for varieties with nef anticanonical bundle

TL;DR

This paper proves that for certain threefold pairs with nef anticanonical bundles, the numerical class of the negative of their canonical divisor plus boundary is always effective, advancing understanding in algebraic geometry.

Contribution

It establishes the effectivity of the numerical class of the negative of the canonical divisor plus boundary for threefold pairs with nef anticanonical bundles, a new result in the field.

Findings

Numerical class of - (K_X + Δ) is effective for threefold pairs with nef - (K_X + Δ).

Results hold under mild singularity assumptions.

Advances the understanding of the nonvanishing problem in algebraic geometry.

Abstract

We prove that if $(X,\Delta)$ is a threefold pair with mild singularities such that ${-}(K_X+\Delta)$ is nef, then the numerical class of ${-}(K_X+\Delta)$ is effective.