We construct a new family of smooth minimal surfaces of general type with K 2 = 7 and p g = 0. We show that for a surface in this family, its canonical divisor is ample and its bicanonical morphism is birational. We also prove that these surfaces satisfy Bloch's conjecture.
We study the construction of complex minimal smooth surfaces S of general type with pg(S) = 0 and K 2 S = 7. Inoue constructed the first examples of such surfaces, which can be described as Galois Z 2 × Z 2 -covers over the four-nodal cubic surface. Later the first named author constructed more examples as Galois Z 2 × Z 2 -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 pg = 0 and K 2 = 7, as Galois Z 2 × Z 2 -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.
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