The Generalised Abundance Conjecture

Let $(X,\Delta)$ be a projective klt pair such that $K_X+\Delta$ is pseudoeffective, and let $L$ be a nef Cartier divisor on $X$. Assume that $K_X+\Delta+L$ is nef.

Generalised Abundance Conjecture. There exists a semiample $\mathbb{Q}$-divisor $M$ such that

$$K_X+\Delta+L\equiv M.$$

This extends abundance from adjoint divisors to adjoint divisors augmented by nef Cartier divisors. The conjecture is used in the paper as an open hypothesis in reductions of Serrano's conjecture.