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We deal with a reducible projective surface with so-called , which are a generalization of normal crossings. First we compute the
of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
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