Tensor fields and connections on holomorphic orbit spaces of finite groups

Abstract

For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\left(\genfrac{}{}{0ex}{}{p}{q}\right)$-tensor field on the principle 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.

15 pages, LaTeX, some arguments rearranged