Generalised Nonvanishing Conjecture

Let $(X,\Delta)$ be a klt pair such that $K_X+\Delta$ is pseudoeffective. Let $L$ be a nef $\mathbb{Q}$-divisor on $X$. Then for every $t\geq0$ the numerical class of the divisor $K_X+\Delta+tL$ belongs to the effective cone.

Generalised Nonvanishing Conjecture. The numerical class of $K_X+\Delta+tL$ belongs to the effective cone for every $t\geq0$.

This conjecture generalises central nonvanishing statements in algebraic geometry and concerns the existence of effective representatives of adjoint divisor classes. The paper develops evidence and proves cases under additional hypotheses, but the conjecture itself is not resolved in the supplied context.