Defect and Hodge numbers of hypersurfaces

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.

25 pages

References in corpus (3)

• The Bott Formula for Toric Varieties
• Cusps and Codes
• Equations of low-degree Projective Surfaces with three-divisible Sets of Cusps

Cited by in corpus (4)

• Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
• Rationally connected non-Fano type varieties
• $2n^2$-inequality for $c{A}_1$ points and applications to birational rigidity
• Defect via differential forms with logarithmic poles