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Actions of compact groups on coherent sheaves

J. Hausen·P. Heinzner
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Abstract

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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J. Hausen, P. Heinzner. 1998-05-28. Actions of compact groups on coherent sheaves. https://arxiv.org/abs/math/9805138

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