In this paper we deal with a reducible projective surface X with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the omega-genus p(X) of X, i.e. the dimension of the vector space of global sections of the dualizing sheaf omega_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 fi bre, then the omega-genus of the fibres is constant.
Calabri, A., Ciliberto, C., Flamini, F., Miranda, R. (2007). On the genus of reducible surfaces and degenerations of surfaces. ANNALES DE L'INSTITUT FOURIER, 57(2), 491-516 [10.5802/aif.2266].
On the genus of reducible surfaces and degenerations of surfaces.
CILIBERTO, CIRO;FLAMINI, FLAMINIO;
2007-01-01
Abstract
In this paper we deal with a reducible projective surface X with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the omega-genus p(X) of X, i.e. the dimension of the vector space of global sections of the dualizing sheaf omega_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 fi bre, then the omega-genus of the fibres is constant.| File | Dimensione | Formato | |
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