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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: In 1980, I. Morrison proved that slope stability of a vector bundle of rank $ 2$ 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 $ \mathcal {O}_{\mathbb{P}E^*}(d)\otimes \pi ^* L^k$, where $ d$ is a positive integer, $ k \gg 0$ and the base manifold is a compact Riemann surface of genus $ g \geq 2$.


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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.

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