Projectivity of analytic Hilbert and Kaehler quotients

Details Projectivity of analytic Hilbert and Kaehler quotients Projectivity of analytic Hilbert and Kaehler quotients

2008-05-26

arxiv.org/abs/0805.3973v2

Trans. Amer. Math. Soc. 362 (2010), no. 6, 3243-3271

Mathematics

Algebraic Geometry

minor changes: title change, typos corrected, obvious issue in the statement of Thm. 3 fixed, revised proof of Prop. 6.6; 25 p

Scientific paper

10.1090/S0002-9947-10-05000-2

We investigate algebraicity properties of quotients of complex spaces by complex reductive Lie groups G. We obtain a projectivity result for compact momentum map quotients of algebraic G-varieties. Furthermore, we prove equivariant versions of Kodaira's Embedding Theorem and Chow's Theorem relative to an analytic Hilbert quotient. Combining these results we derive an equivariant algebraisation theorem for complex spaces with projective quotient.

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