Representations on the cohomology of smooth projective hypersurfaces with symmetries

Details Representations on the cohomology of smooth projective hypersurfaces with symmetries Representations on the cohomology of smooth projective hypersurfaces with symmetries

2009-08-12

arxiv.org/abs/0908.1748v2

Mathematics

Algebraic Geometry

14 pages; Lemma 2.6 removed to make argument clearer + minor revisions

Scientific paper

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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