Defect and Hodge numbers of hypersurfaces

Abstract

Abstract We define defect for hypersurfaces with A-D-E singularities in complex projective normal Cohen–Macaulay fourfolds having some vanishing properties of Bott-type and prove formulae for Hodge numbers of big resolutions of such hypersurfaces. We compute Hodge numbers of Calabi–Yau manifolds obtained as small resolutions of cuspidal triple sextics and double octics with higher A j singularities.