Orbifold Hodge numbers of Calabi–Yau hypersurfaces

Abstract

We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an n-dimensional simplicial Fano toric variety and then explicitly compute h 1,1 orb and h n-2,1 orb for the hypersurface. We give applications to the orbifold string theory conjecture and orbifold mirror symmetry.