Smooth minimal surfaces of general type with p g = 0, K ² = 7 and involutions

Lee and the second named author studied involutions on smooth minimal surfaces S of general type with [Formula: see text]([Formula: see text]) = 0 and [Formula: see text] = 7. They gave the possibilities of the birational models [Formula: see text] of the quotients and the branch divisors [Formula: see text] induced by involutions [Formula: see text] on the surfaces [Formula: see text]. In this paper we improve and refine the results of Lee and the second named author. We exclude the case of the Kodaira dimension [Formula: see text] = 1 when the number [Formula: see text] of isolated fixed points of an involution [Formula: see text] on [Formula: see text] is nine. The possibilities of branch divisors [Formula: see text] are reduced for the case [Formula: see text] = 9, and are newly given for the case [Formula: see text] = 11. Moreover, we show that if the branch divisor [Formula: see text] has three irreducible components, then [Formula: see text] is an Inoue surface.