Using Reider's method, we analyse the adjunction mappings on general-type surfaces with pg = 0, q = 0, cj = 4 and even intersection form. In particular, we prove that when the funda-mental group of such a surface does not have any irreducible SU(2) or SO(3)-representations, there exists a divisor numerically equivalent to the canonical divisor so that its adjunction map is a regular bimeromorphism.
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