Survey of conifold transitions between Calabi-Yau threefolds with a sketched differential-geometric proof of the necessity part of Friedman's smoothing criterion.
Deformations of Compact Calabi--Yau Conifolds
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abstract
Let $X$ be a compact normal K\"ahler space whose canonical sheaf is a rank-one free $\mathcal O_X$ module and whose singularities are isolated, rational and quasi-homogeneous. We prove then that under a topological hypothesis the obstruction to deforming $X$ concentrates upon its singularities, generalizing partially the results of Namikawa--Gross. We prove also that under a certain hypothesis the locally trivial deformations of $X$ are unobstructed.
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An introduction to conifold transitions
Survey of conifold transitions between Calabi-Yau threefolds with a sketched differential-geometric proof of the necessity part of Friedman's smoothing criterion.