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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Projectivity of analytic Hilbert and Kähler quotients
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by Daniel Greb PDF
Trans. Amer. Math. Soc. 362 (2010), 3243-3271


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
  • MR Author ID: 888778
  • Email:
  • 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
  • © Copyright 2010 Daniel Greb
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 3243-3271
  • MSC (2000): Primary 14L30, 14L24; Secondary 32M05, 53D20
  • DOI:
  • MathSciNet review: 2592955