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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Decomposing representations of finite groups on Riemann-Roch spaces


Authors: David Joyner and Amy Ksir
Journal: Proc. Amer. Math. Soc. 135 (2007), 3465-3476
MSC (2000): Primary 14H37
Published electronically: July 27, 2007
MathSciNet review: 2336559
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Abstract: If $ G$ is a finite subgroup of the automorphism group of a projective curve $ X$ and $ D$ is a divisor on $ X$ stabilized by $ G$, then we compute a simplified formula for the trace of the natural representation of $ G$ on the Riemann-Roch space $ L(D)$, under the assumption that $ L(D)$ is ``rational'', $ D$ is nonspecial, and the characteristic is ``good''. We discuss the partial formulas that result if $ L(D)$ is not rational.


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Additional Information

David Joyner
Affiliation: Mathematics Department, United States Naval Academy, Annapolis, Maryland 21402
Email: wdj@usna.edu

Amy Ksir
Affiliation: Mathematics Department, United States Naval Academy, Annapolis, Maryland 21402
Email: ksir@usna.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08967-8
PII: S 0002-9939(07)08967-8
Received by editor(s): February 10, 2004
Received by editor(s) in revised form: August 21, 2006
Published electronically: July 27, 2007
Additional Notes: The first author was supported in part by an NSA-MSP grant.
The second author was supported in part by a USNA-NARC grant.
Communicated by: Michael Stillman
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.