On the genus of reducible surfaces and degenerations of surfaces
Copyright policy )On the genus of reducible surfaces and degenerations of surfaces
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.
- University of Ferrara Italy
- Colorado State University United States
- University of Rome Tor Vergata Italy
Degenerations of surfaces; singularities; birational geometry; topological invariants, degeneration of surfaces, topological invariants, Settore MAT/03 - GEOMETRIA, Families, moduli, classification: algebraic theory, Degenerations, families of surfaces, topological invariants, families of surfaces, Singularities of surfaces or higher-dimensional varieties, Degenerations, Fibrations, degenerations in algebraic geometry
Degenerations of surfaces; singularities; birational geometry; topological invariants, degeneration of surfaces, topological invariants, Settore MAT/03 - GEOMETRIA, Families, moduli, classification: algebraic theory, Degenerations, families of surfaces, topological invariants, families of surfaces, Singularities of surfaces or higher-dimensional varieties, Degenerations, Fibrations, degenerations in algebraic geometry
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