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Smoothing nodal Calabi-Yau n-folds

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arxiv 0810.0141 v3 pith:Y47HFQR2 submitted 2008-10-01 math.AG math.DG

S. Rollenske , R. P. Thomas This is my paper · ORCID
classification math.AGmath.DG
keywords calabi-yauconversefriedmanhomologynodalsmoothingclassesdimensional
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Let X be an n-dimensional Calabi-Yau with ordinary double points, where n is odd. Friedman showed that for n=3 the existence of a smoothing of X implies a specific type of relation between homology classes on a resolution of X. (The converse is also true, due to work of Friedman, Kawamata and Tian.) We sketch a more topological proof of this result, and then extend it to higher dimensions. For n>3 the "Yukawa product" on the middle dimensional (co)homology plays an unexpected role. We also discuss a converse, proving it for nodal Calabi-Yau hypersurfaces in projective space.

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  1. Calabi-Yau threefolds across quadratic singularities

    math.DG 2025-01 unverdicted

    This paper is a survey of the geometry of conifold transitions between Calabi-Yau threefolds, focusing on non-Kähler outputs and the structures they carry.

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