The minimal-volume conjecture for log canonical pairs with reduced boundary

Let $(X,B)$ be a projective log canonical pair of dimension $n$, where $B$ is a nonzero reduced divisor and $K_X+B$ is ample. The volume of $K_X+B$ is the top self-intersection number $(K_X+B)^n$. The paper constructs such a pair in every dimension, with volume as described in Theorem 1. Minimal-volume conjecture. For every integer $n\geq 2$, the constructed pair has the smallest volume among all projective log canonical pairs $(X,B)$ of dimension $n$ with $B$ a nonzero reduced divisor and $K_X+B$ ample. The surface case is known, while the assertion in higher dimensions remains open.