For minimal general-type surfaces with pg=0 and K^2=7, the paper gives explicit short lists of possible quotient branch divisors for involutions with 9 or 11 fixed points and shows the three-component case characterizes Inoue surfaces.
Chen, Commuting involutions on surfaces of general type with pg = 0 and K 2 = 7, Manuscripta math
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Smooth minimal surfaces of general type with $p_g=0, K^2=7$ and involutions
For minimal general-type surfaces with pg=0 and K^2=7, the paper gives explicit short lists of possible quotient branch divisors for involutions with 9 or 11 fixed points and shows the three-component case characterizes Inoue surfaces.