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arXiv · 0810.0141

Smoothing nodal Calabi-Yau n-folds

S. Rollenske·R. P. Thomas
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Abstract

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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S. Rollenske, R. P. Thomas. 2008-10-01. Smoothing nodal Calabi-Yau n-folds. https://doi.org/10.1112/jtopol%2Fjtp016

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