Orbifoldes à premi\ere classe de Chern nulle

Details Orbifoldes à premi\ere classe de Chern nulle Orbifoldes à premi\ere classe de Chern nulle

2004-02-14

arxiv.org/abs/math/0402243v2

Mathematics

Algebraic Geometry

Scientific paper

An orbifold version of Bogomolov decomposition theorem is established for compact K\"ahler spaces with quotient singularities and first Chern class zero.The proof is a direct adaptation of the classical smooth case, using Ricci-flat K\"ahler metrics, and Cheeger-Gromoll splitting theorem. It implies that normal K3 surfaces are uniformised in the orbifold sense either by normal K3 surfaces or by a complex torus, as conjectured by D.Q. Zhang. It also implies some conjectures on "special" threefolds raised in math.AG/0110051

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