Orbifoldes \`a premi\ere classe de Chern nulle
Algebraic Geometry
2007-05-23 v2 Complex Variables
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
Cite
@article{arxiv.math/0402243,
title = {Orbifoldes \`a premi\ere classe de Chern nulle},
author = {Frederic Campana},
journal= {arXiv preprint arXiv:math/0402243},
year = {2007}
}