Moduli of Gorenstein ℚ-homology projective planes

Abstract

We give a complete classification of complex ℚ-homology projective planes with numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all moduli curves are rational and defined over ℚ, and we determine all families explicitly using extremal rational elliptic surfaces and Enriques involutions of base change type.