
Journal of Lie Theory 13 (2003), No. 2, 519534 Copyright Heldermann Verlag 2003 Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups Andreas Kriegl Institut f. Mathematik, Universität Wien, Strudlhofgasse 4, 1090 Wien, Austria Mark Losik Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia Peter W. Michor Institut f. Mathematik, Universität 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 Ginvariant 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 [ Fulltextpdf (283 KB)] for subscribers only. 