Balanced metrics and Chow stability of projective bundles over Riemann surfaces

Author:
Reza Seyyedali

Journal:
Proc. Amer. Math. Soc. **141** (2013), 2841-2853

MSC (2010):
Primary 32Q26; Secondary 53C07

DOI:
https://doi.org/10.1090/S0002-9939-2013-11548-0

Published electronically:
May 1, 2013

MathSciNet review:
3056574

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Abstract | References | Similar Articles | Additional Information

Abstract: In 1980, I. Morrison proved that slope stability of a vector bundle of rank over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. In a previous work, we generalized Morrison's result to higher rank vector bundles over compact algebraic manifolds of arbitrary dimension that admit a constant scalar curvature metric and have a discrete automorphism group. In this article, we give a simple proof for polarizations , where is a positive integer, and the base manifold is a compact Riemann surface of genus .

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Additional Information

**Reza Seyyedali**

Affiliation:
Department of Mathematics, University of California, Irvine, California 92697

Address at time of publication:
Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1

Email:
rseyyeda@math.uci.edu, rseyyedali@uwaterloo.ca

DOI:
https://doi.org/10.1090/S0002-9939-2013-11548-0

Received by editor(s):
November 28, 2010

Received by editor(s) in revised form:
November 11, 2011

Published electronically:
May 1, 2013

Communicated by:
Michael Wolf

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.