Projectivity of analytic Hilbert and Kaehler quotients

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.

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

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• Variation of Gieseker moduli spaces via quiver GIT
• Moduli of polarised manifolds via canonical Kähler metrics
• Complex-analytic quotients of algebraic G-varieties
• Compact Kaehler quotients of algebraic varieties and Geometric Invariant Theory
• Kempf-Ness type theorems and Nahm equations
• Invariant meromorphic functions on Stein spaces
• Reductive quotients of klt singularities