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On the extendability of elliptic surfaces of rank two and higher

Angelo Felice Lopez, Roberto Muñoz, José Carlos Sierra (2009)

Annales de l’institut Fourier

We study threefolds X r having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many embeddings...

On the genus of reducible surfaces and degenerations of surfaces

Alberto Calabri, Ciro Ciliberto, Flaminio Flamini, Rick Miranda (2007)

Annales de l’institut Fourier

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 p ω ( X ) of X , i.e. the dimension of the vector space of global sections of the dualizing sheaf ω X . Then we prove that, when X is smoothable, i.e. when X is the central fibre of a flat family π : 𝒳 Δ parametrized by a disc, with smooth general fibre, then the ω -genus of the fibres of π is constant.

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