Minimal-volume canonical Calabi–Yau hypersurface conjecture

Let $s_0=2$ and $s_m=s_{m-1}(s_{m-1}-1)+1$ for $m\geq 1$ be Sylvester's sequence. For a positive integer $n$, set

$$d=(2s_n-3)(s_n-1).$$

A general hypersurface $X$ of degree $d$ in the weighted projective space

$$\mathbb{P}^{n+1}(d/s_0,\ldots,d/s_{n-1},s_n-1,s_n-2)$$

is a canonical Calabi–Yau $n$-fold, with ample Weil divisor $\mathcal{O}_X(1)$. Minimal-volume canonical Calabi–Yau hypersurface conjecture. The divisor $\mathcal{O}_X(1)$ has minimal volume among ample Weil divisors on canonical Calabi–Yau $n$-folds. The conjecture is motivated by the fact that the examples have minimal volume in the low dimensions discussed in the paper, but its general validity remains open.