Tensor fields and connections on holomorphic orbit spaces of finite groups

Details Tensor fields and connections on holomorphic orbit spaces of finite groups Tensor fields and connections on holomorphic orbit spaces of finite groups

2002-03-08

arxiv.org/abs/math/0203079v2

J. Lie Theory 13 (2003), 519--534

Mathematics

Differential Geometry

15 pages, LaTeX, some arguments rearranged

Scientific paper

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 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.

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