Projectivity of analytic Hilbert and Kaehler quotients

TL;DR

This paper studies the algebraic and projective properties of quotients of complex spaces by reductive groups, establishing new theorems that connect analytic and algebraic quotients and providing conditions for their projectivity.

Contribution

It introduces new results on the projectivity of momentum map quotients and extends classical theorems to equivariant settings for complex spaces with algebraic group actions.

Findings

Proves projectivity of compact momentum map quotients.

Establishes equivariant versions of Kodaira's Embedding and Chow's Theorems.

Derives an algebraisation theorem for complex spaces with projective 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.