Defect via differential forms with logarithmic poles

We study type III contractions of Calabi–Yau threefolds containing a ruled surface over a smooth curve. We discuss the conditions necessary for the image threefold to be smoothable. We describe the change in Hodge numbers caused by this contraction and smoothing deformation. A generalization of a formula for calculating Hodge numbers of hypersurfaces in [Formula: see text] with ordinary double and triple points is presented. We use these results to construct new Calabi–Yau threefolds of Picard rank two arising from a family of quintic threefolds containing a cone.

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Hodge numbers of hypersurfaces in ℙ⁴ with ordinary triple points

Cynk

2021

Advances in Geometry

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Defect via differential forms with logarithmic poles

Abstract: Abstract. We prove formulae for the Hodge numbers of big resolutions of singular hypersurfaces satisfying a Bott-type vanishing condition.

Cited by 3 publications

References 21 publications

Defect formula for nodal complete intersection threefolds

Defect formula for nodal complete intersection threefolds

Type III contractions and quintic threefolds

Hodge numbers of hypersurfaces in ℙ⁴ with ordinary triple points

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Defect via differential forms with logarithmic poles

Abstract: Abstract. We prove formulae for the Hodge numbers of big resolutions of singular hypersurfaces satisfying a Bott-type vanishing condition.

Cited by 3 publications

References 21 publications

Defect formula for nodal complete intersection threefolds

Defect formula for nodal complete intersection threefolds

Type III contractions and quintic threefolds

Hodge numbers of hypersurfaces in ℙ4 with ordinary triple points

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Product

Resources

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Hodge numbers of hypersurfaces in ℙ⁴ with ordinary triple points