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The Picard group of a complex quotient variety. (English) Zbl 0699.14004

Consider a Stein complex space X, a reductive connected complex group G acting holomorphically on X and let X//G denote the categorical quotient (which has a structure of Stein space). The aim of this paper is to prove that the natural map Pic(X//G)\(\to Pic(X)\) is injective in each of the following situations: \((1)\quad G\quad is\) semisimple; and \((2)\quad X\quad is\) smooth and the radical of G has a fixed point on X.
Reviewer: A.Buium

MSC:

14C22 Picard groups
14M17 Homogeneous spaces and generalizations
32M10 Homogeneous complex manifolds
14L30 Group actions on varieties or schemes (quotients)
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References:

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