Geodesic
Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups
Andreas Kriegl1 ; Mark Losik2 ; Peter W. Michor1, 3, 4, 5, 6
1Institut f. Mathematik, Universität Wien, Strudlhofgasse 4, 1090 Wien, Austria
2Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia
3For 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.
4Keywords: Complex orbifolds, orbit spaces of complex finite group actions.
5MSC: 32M17
6[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 519-534

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 32M17
Mots-clés : Complex orbifolds, orbit spaces of complex finite group actions

Andreas Kriegl  1   ; Mark Losik  2   ; Peter W. Michor  1 , 3 , 4 , 5 , 6

1 Institut f. Mathematik, Universität Wien, Strudlhofgasse 4, 1090 Wien, Austria
2 Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia
3 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.
4 Keywords: Complex orbifolds, orbit spaces of complex finite group actions.
5 MSC: 32M17
6 [ 
Andreas Kriegl; Mark Losik; Peter W. Michor. Tensor Fields and Connections on Holomorphic Orbit Spaces of Finite Groups. Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 519-534. http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a12/
@article{JOLT_2003_13_2_a12,
     author = {Andreas Kriegl and Mark Losik and Peter 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a12/}
}
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