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Projectivity of analytic Hilbert and Kähler quotients


Author: Daniel Greb
Journal: Trans. Amer. Math. Soc. 362 (2010), 3243-3271
MSC (2000): Primary 14L30, 14L24; Secondary 32M05, 53D20
DOI: https://doi.org/10.1090/S0002-9947-10-05000-2
Published electronically: January 20, 2010
MathSciNet review: 2592955
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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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Additional Information

Daniel Greb
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
Address at time of publication: Fakultät für Mathematik, Abteilung für Reine Mathematik, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
Email: daniel.greb@math.uni-freiburg.de

DOI: https://doi.org/10.1090/S0002-9947-10-05000-2
Received by editor(s): September 2, 2008
Published electronically: January 20, 2010
Additional Notes: The author was supported by the Studienstiftung des deutschen Volkes and by SFB/TR 12 “Symmetries and Universality of Mesoscopic Systems” of the DFG
Article copyright: © Copyright 2010 Daniel Greb

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