Gentle $m$-Calabi–Yau tilted algebras

We prove that all gentle 2-Calabi–Yau tilted algebras are Jacobian, moreover their bound quiver can be obtained via block decomposition. For two related families, the $m$-cluster-tilted algebras of type $\mathbb{A}$ and $\tilde{\mathbb{A}}$, we prove that a module $M$ is stable Cohen-Macaulay if and only if $\Omega^{m+1} \tau M \simeq M$.