Orbifoldes \`a premi\ere classe de Chern nulle

Publication date: 14 February 2004

Abstract: 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

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Other complex differential geometry (53C56) Generalizations (algebraic spaces, stacks) (14A20) Differential spaces (58A40)

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