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Note on the stability of principal bundles

Author(s): Donghoon Hyeon; David Murphy
Journal: Proc. Amer. Math. Soc. 132 (2004), 2205-2213.
MSC (2000): Primary 14D20
Posted: March 10, 2004
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Abstract: We compare various notions of stability for principal bundles, and show that over a compact Riemann surface of genus greater than 2, there exist principal $\operatorname{SL}(2)$-bundles that are Ad-stable.

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M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540-567. MR 32:1725

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A. Ramanathan, Stable principal bundles on a compact Riemann surface, Math. Ann. 213 (1975), 129-152. MR 51:5979

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Additional Information:

Donghoon Hyeon
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Address at time of publication: Department of Mathematics, Rice University, 6100 Main St., Houston, Texas 77005
Email: hyeon@math.rice.edu

David Murphy
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Email: dcmurphy@math.uiuc.edu

DOI: 10.1090/S0002-9939-04-07386-1
PII: S 0002-9939(04)07386-1
Received by editor(s): February 18, 2002
Received by editor(s) in revised form: February 18, 2003
Posted: March 10, 2004
Communicated by: Michael Stillman
Copyright of article: Copyright 2004, American Mathematical Society

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