The Borisov–Alexeev–Borisov conjecture for quasismooth weighted complete intersections

Let $m$ and $\epsilon$ be fixed positive numbers, let $\alpha$ be a negative integer, and consider quasismooth weighted complete intersections of dimension $m$ and amplitude $\alpha$ having only $\epsilon$-klt singularities. Borisov–Alexeev–Borisov conjecture. There exist only finitely many families of such quasismooth weighted complete intersections. The statement extends the boundedness expectations of the Borisov–Alexeev–Borisov conjecture from the usual setting to quasismooth weighted complete intersections; its resolution is not given in the supplied text.