Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

On the converse to a theorem of Atiyah and Bott


Authors: Robert Friedman and John W. Morgan
Journal: J. Algebraic Geom. 11 (2002), 257-292
Published electronically: November 19, 2001
MathSciNet review: 1874115
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Abstract | References | Additional Information

Abstract: Let $G$ be a complex reductive group and let $C$be a smooth curve of genus at least one. We prove a converse to a theorem of Atiyah-Bott concerning the stratification of the space of holomorphic $G$-bundles on $C$. In case the genus of $C$ is one, we establish that there is a stratification in the strong sense. The paper concludes with a characterization of the minimally unstable strata in case $G$ is simple


References [Enhancements On Off] (What's this?)

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  • 3. N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5, et 6, Masson, Paris, 1981.
  • 4. R. Friedman and J.W. Morgan, Holomorphic principal bundles over elliptic curves, math.AG/9811130.
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Additional Information

Robert Friedman
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: rf@math.columbia.edu

John W. Morgan
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: jm@math.columbia.edu

DOI: https://doi.org/10.1090/S1056-3911-01-00304-6
Received by editor(s): June 19, 2000
Published electronically: November 19, 2001
Additional Notes: The first author was partially supported by NSF grant DMS-99-70437. The second author was partially supported by NSF grant DMS-97-04507.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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