Projectivity of analytic Hilbert and Kähler quotients

Greb, Daniel

doi:10.1090/S0002-9947-10-05000-2

Projectivity of analytic Hilbert and Kähler quotients
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by Daniel Greb

Trans. Amer. Math. Soc. 362 (2010), 3243-3271

DOI: https://doi.org/10.1090/S0002-9947-10-05000-2

Published electronically: January 20, 2010

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Abstract:

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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