Actions of compact groups on coherent sheaves

Details Actions of compact groups on coherent sheaves Actions of compact groups on coherent sheaves

1998-05-28

arxiv.org/abs/math/9805138v1

Transformation Groups, Vol. 4, No.1, 25-34 (1999)

Mathematics

Complex Variables

9 pages, plain tex

Scientific paper

Let K be a compact Lie group and G its complexification. For a not necessarily reduced Stein K-space X we show that there is a complex space Z endowed with a holomorphic action of the universal complexification G of K that contains X as an open K-stable subset. The correspondence is functorial. As our main result we prove that every coherent K-sheaf on X extends uniquely to a G-sheaf on Z.

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