We deal with a reducible projective surface X with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the ω-genus of X, i.e. the dimension of the vector space of global sections of the dualizing sheaf ω of X. Then we prove that, when X is smoothable, i.e. when X is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the ω-genus of the fibres of the family is constant.
On the genus of reducible surfaces and degenerations of surfaces
CALABRI, Alberto;
2007
Abstract
We deal with a reducible projective surface X with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the ω-genus of X, i.e. the dimension of the vector space of global sections of the dualizing sheaf ω of X. Then we prove that, when X is smoothable, i.e. when X is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the ω-genus of the fibres of the family is constant.File in questo prodotto:
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