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On glueing curves on surfaces and zero cycles

Hursit Önsiper (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The structure of the group H 2 X , K 2 of a surface X with prescribed singularities is investigated.

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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