Definition 2.11 Let $m\geqslant 2$. An almost Calabi–Yau $m$-fold, or ACY $m$-fold for short, is a quadruple $(X,J,\omega,\Omega)$ such that $(X,J)$ is a compact $m$-dimensional complex manifold, $\omega$ is the Kähler form of a Kähler metric $g$ on $X$, and $\Omega$ is a non-vanishing holomorphic $(m,0)$-form on $X$.