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arXiv · 0908.1748

Representations on the cohomology of smooth projective hypersurfaces with symmetries

Gabriel Chênevert
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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 about 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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Gabriel Chênevert. 2009-08-12. Representations on the cohomology of smooth projective hypersurfaces with symmetries. https://arxiv.org/abs/0908.1748

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