Tensor fields and connections on holomorphic orbit spaces of finite groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63523For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on the principle 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.15 pages, LaTeX, some arguments rearrangedDifferential GeometryComplex VariablesRepresentation Theory32M17Tensor fields and connections on holomorphic orbit spaces of finite groupstext