MMP for Enriques pairs and singular Enriques varieties

We introduce and study the class of primitive Enriques varieties, whose smooth members are Enriques manifolds. We provide several examples and we demonstrate that this class is stable under the operations of the Minimal Model Program (MMP). In particular, given an Enriques manifold $Y$ and an effective $\mathbb{R}$-divisor $B_Y$ on $Y$ such that the pair $(Y,B_Y)$ is log canonical, we prove that any $(K_Y+B_Y)$-MMP terminates with a minimal model $(Y^{\mathrm{\prime }},B_{Y^{\mathrm{\prime }}})$ of $(Y,B_Y)$, where $Y^{\mathrm{\prime }}$ is a $\mathbb{Q}$-factorial primitive Enriques variety with canonical singularities. Finally, we investigate the asymptotic theory of Enriques manifolds.