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Orbifold Hodge numbers of Calabi-Yau hypersurfaces. (English) Zbl 1052.32018
The author shows that the orbifold Hodge numbers of a generic Calabi-Yau hypersurface in a complex $$4$$-dimensional simplicial Fano toric variety coincide with the Hodge numbers of its smooth crepant resolution. After reviewing the relevant facts from orbifold cohomology and toric geometry, the author finds characterizations for the twisted sectors of complete simplicial Fano toric varieties. Then he computes formulas for some orbifold Hodge numbers of these hypersurfaces. At the end he presents some examples.

##### MSC:
 32Q25 Calabi-Yau theory (complex-analytic aspects) 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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