We define and study a concrete stratification of the moduli space of Gorenstein stable surfaces X satisfying K_X^2 = 2 and χ(O_X ) = 4, by first establishing an isomorphism with the moduli space of plane octics with certain singularities, which is then easier to handle concretely. In total, there are 47 inhabited strata with altogether 78 components.
stable surfacesGorenstein singularitiesAlgebraische Flächen vom allgemeinen typsemi log canonical singularitiesGorenstein SingularitätenAlgebraische Flächenmoduli spacesstabile Flächensemi-log-kanonische SingularitätenAlgebraic surfacesAlgebraic surfaces of general type