Journal of Lie Theory Vol. 13, No. 2, pp. 519534 (2003) 

Tensor fields and connections on holomorphic orbit spaces of finite groupsAndreas Kriegl, Mark Losik, and Peter W. MichorA.\ KrieglInstitut für Mathematik Universität Wien Strudlhofgasse 4, A1090 Wien Austria Andreas.Kriegl@univie.ac.at, P.\ W.\ Michor Institut für Mathematik Universität Wien Strudlhofgasse 4, A1090 Wien Austria and Erwin Schrödinger Institut für Mathematische Physik Boltzmanngasse 9, A1090 Wien Austria Peter.Michor@esi.ac.at, and M. Losik Saratov State University ul. Astrakhanskaya, 83 410026 Saratov, Russia LosikMV@info.sgu.ru Abstract: For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic ${p\choose q}$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. Full text of the article:
Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.
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