Abstract
We study the projective normality of a minimal surface X which is a ramified double covering over a rational surface S with dim|−KS|≥1. In particular Horikawa surfaces, the minimal surfaces of general type with KX2=2pg(X)−4, are of this type, up to resolution of singularities. Let π be the covering map from X to S. We show that the Z2-invariant adjoint divisors KX+rπ⁎A are normally generated, where the integer r≥3 and A is an ample divisor on S.
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