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Journal of Lie Theory 13 (2003), No. 2, 519--534
Copyright Heldermann Verlag 2003



Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups

Andreas Kriegl
Institut f. Mathematik, Universitšt Wien, Strudlhofgasse 4, 1090 Wien, Austria

Mark Losik
Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia

Peter W. Michor
Institut f. Mathematik, Universitšt Wien, Strudlhofgasse 4, 1090 Wien, Austria



For a representation of a finite group G on a complex vector space V we determine when a holomorphic (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.

MSC: 32M17

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