Representations on the cohomology of smooth projective hypersurfaces with symmetries
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- by Gabriel Chênevert PDF
- Proc. Amer. Math. Soc. 141 (2013), 1185-1197 Request permission
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.References
- Armand Borel and Jean-Pierre Serre, Le théorème de Riemann-Roch, Bull. Soc. Math. France 86 (1958), 97–136 (French). MR 116022, DOI 10.24033/bsmf.1500
- Gabriel Chenevert, Exponential sums, hypersurfaces with many symmetries and Galois representations, ProQuest LLC, Ann Arbor, MI, 2008. Thesis (Ph.D.)–McGill University (Canada). MR 2714096
- Peter Donovan, The Lefschetz-Riemann-Roch formula, Bull. Soc. Math. France 97 (1969), 257–273. MR 263834, DOI 10.24033/bsmf.1680
- William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249, DOI 10.1007/978-1-4612-0979-9
- F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
- Minoru Nakaoka, Note on the Lefschetz fixed point theorem, Osaka Math. J. 6 (1969), 135–142. MR 266207
- Darrell R. Shreve, On a certain class of symmetric hypersurfaces, Bull. Amer. Math. Soc. 45 (1939), 948–951. MR 1021, DOI 10.1090/S0002-9904-1939-07123-1
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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1185-1197
- MSC (2010): Primary 14Q10, 19L10, 20C30
- DOI: https://doi.org/10.1090/S0002-9939-2012-11431-5
- MathSciNet review: 3008866