Representations on the cohomology of hypersurfaces and mirror symmetry

Details Representations on the cohomology of hypersurfaces and mirror symmetry Representations on the cohomology of hypersurfaces and mirror symmetry

2010-04-20

arxiv.org/abs/1004.3446v1

Mathematics

Representation Theory

34 pages

Scientific paper

We study the representation of a finite group acting on the cohomology of a non-degenerate, invariant hypersurface of a projective toric variety. We deduce an explicit description of the representation when the toric variety has at worst quotient singularities. As an application, we conjecture a representation-theoretic version of Batyrev and Borisov's mirror symmetry between pairs of Calabi-Yau hypersurfaces, and prove it when the hypersurfaces are both smooth or have dimension at most 3. An interesting consequence is the existence of pairs of Calabi-Yau orbifolds whose Hodge diamonds are mirror, with respect to the usual Hodge structure on singular cohomology.

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