Andreas Kriegl, Mark Losik, Peter W. Michor
Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups
The paper is published: J. Lie Theory 13 (2003) 519-534

MSC:

32M05 Complex Lie groups, automorphism groups of complex spaces, See also {22E10}

Abstract: For a representation of a finite group $G$ on a complex vector space
$V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on
the principal stratum of the orbit space $V/G$ can be lifted to a
holomorphic $G$-invariant tensor field on $V$. This extends also to
connections. As a consequence we determine those holomorphic
diffeomorphisms on $V/G$ which can be lifted to orbit preserving
holomorphic diffeomorphisms on $V$. This in turn
is applied to characterize complex orbifolds.
Keywords: complex orbifolds, orbit spaces of complex finite group actions
Notes: second version