On the minimal model of semi-isogenous mixed surfaces

The aim of this note is to determine the minimal models of the semi-isogenous mixed surfaces with χ (O)=1 χ ( O ) = 1 and K²>0 K 2 > 0 constructed in [11]. In order to do this, we further develop the idea of orbit divisors , introduced in [13] to construct effective divisors on surfaces isogenous to a product of mixed type, extending it to semi-isogenous mixed surfaces.