On analytic abelian coverings (Q1086302)

We consider abelian coverings \(f: (X,0)\to (Y,0)\) of n-dimensional complex analytic singularities, with normal total spaces (X,0). Under quite general assumptions on the base space (Y,0) and on the corresponding branching set (D,0)\(\subset (Y,0)\), we show that these coverings can be described as pull-backs of coverings with base space \(({\mathbb{C}}^ m,0)\) and branching set the union of the coordinate hyperplanes, where m is the number of irreducible components of (D,0). - These special coverings over \(({\mathbb{C}}^ m,0)\) are related to abelian quotient singularities in a similar way as the well-known case of Hirzebruch-Jung singularities \((m=2).\) As an application, we describe the global abelian coverings \(\phi: V\to W\) among projective varieties (for large classes of base spaces W) in terms of finite abelian quotients of weighted projective varieties.