Journal of Lie Theory

no. 2
Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups
Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 519-534
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.
DOI: 10.5802/jolt.318
Classification: 32M17
Keywords: Complex orbifolds, orbit spaces of complex finite group actions 
@article{JOLT_2003_13_2_a12,
     author = {A. Kriegl and M. Losik and P. W. Michor},
     title = {Tensor {Fields} and {Connections} on {Holomorphic} {Orbit} {Spaces} of {Finite} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {519--534},
     year = {2003},
     volume = {13},
     number = {2},
     doi = {10.5802/jolt.318},
     zbl = {1039.32029},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.318/}
}
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%A M. Losik
%A P. W. Michor
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%J Journal of Lie Theory
%D 2003
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A. Kriegl; M. Losik; P. W. Michor. Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups. Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 519-534. doi: 10.5802/jolt.318

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