Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A simple proof for the finiteness of GIT-quotients
HTML articles powered by AMS MathViewer

by Alexander Schmitt PDF
Proc. Amer. Math. Soc. 131 (2003), 359-362 Request permission

Abstract:

Let $G\times X\longrightarrow X$ be an action of the reductive group $G$ on the projective scheme $X$. For every linearization $\sigma$ of this action in an ample line bundle, there is an open set $X_\sigma ^{\mathrm {ss}}$ of $\sigma$-semistable points. We provide an elementary and geometric proof for the fact that there exist only finitely many open sets of the form $X_\sigma ^{\mathrm {ss}}$. This observation was originally due to Białynicki-Birula and Dolgachev and Hu.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14L24, 14L30
  • Retrieve articles in all journals with MSC (1991): 14L24, 14L30
Additional Information
  • Alexander Schmitt
  • Affiliation: Universität GH Essen, FB6 Mathematik & Informatik, D-45117 Essen, Germany
  • MR Author ID: 360115
  • ORCID: 0000-0002-4454-1461
  • Received by editor(s): April 17, 2001
  • Received by editor(s) in revised form: September 17, 2001
  • Published electronically: June 3, 2002
  • Communicated by: Michael Stillman
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 359-362
  • MSC (1991): Primary 14L24, 14L30
  • DOI: https://doi.org/10.1090/S0002-9939-02-06599-1
  • MathSciNet review: 1933324