A two-dimensional family of surfaces of general type with pg=0 and K2=7

We study the construction of complex minimal smooth surfaces S of general type with p(g)(S) = 0 and K-S(2) = 7. Inoue constructed the first examples of such surfaces, which can be described as Galois Z/2Z x Z/2Z-covers over the four-nodal cubic surface. Later the first named author constructed more examples as Galois Z/2Z x Z/2Z-covers over certain six-nodal del Pezzo surfaces of degree one. In this paper we construct a two-dimensional family of minimal smooth surfaces of general type with p(g) = 0 and K-2 = 7, as Galois Z/2Z x Z/2Z-covers of certain rational surfaces with Picard number three, with eight nodes and with two elliptic fibrations. This family is different from the previous ones. (C) 2020 Elsevier Inc. All rights reserved.