Borisov–Alexeev–Borisov boundedness conjecture for Fano varieties

Let $n$ be a positive integer. Consider a $\mathbb{Q}$-factorial terminal Fano variety $X$ of Picard number $1$, with dimension at most $n$.

Borisov–Alexeev–Borisov conjecture. There is a positive number $\delta(n)$ such that

$$(-K_X)^{\dim X}\leq\delta(n).$$

This is a boundedness assertion for low-dimensional terminal Fano varieties. The conjecture is a special case of the Borisov–Alexeev–Borisov boundedness problem and is used as an input for analyzing exceptional sets and $a$-constants.