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

 

Representations on the cohomology of smooth projective hypersurfaces with symmetries


Author: Gabriel Chênevert
Journal: Proc. Amer. Math. Soc. 141 (2013), 1185-1197
MSC (2010): Primary 14Q10, 19L10, 20C30
Published electronically: August 29, 2012
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Abstract: This paper is concerned with the primitive cohomology of a smooth projective hypersurface considered as a linear representation for its automorphism group. Using the Lefschetz-Riemann-Roch formula, the character of this representation is described on each piece of the Hodge decomposition. A consequence concerning the existence of smooth symmetric hypersurfaces that are stable under the standard irreducible permutation representation of the symmetric group on homogeneous coordinates is drawn.


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Additional Information

Gabriel Chênevert
Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Nederland
Address at time of publication: ISÉN (Université Catholique de Lille), 41 Vauban, 59046 Lille Cedex, France
Email: gabriel.chenevert@isen.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11431-5
PII: S 0002-9939(2012)11431-5
Received by editor(s): January 19, 2010
Received by editor(s) in revised form: August 17, 2011
Published electronically: August 29, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.