The Coble-Mukai lattice from $\mathbb{Q}$-Gorenstein deformations

We show some geometric properties of Enriques surfaces via $\mathbb{Q}$-Gorenstein smoothings of Coble surfaces. In particular, we explicitly identify the Enriques lattice of the general fiber with the Coble-Mukai lattice. At the end, we discuss applications to Gorenstein $\mathbb{Q}$-Homology projective planes with trivial canonical class.