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Quotients of the conifold in compact Calabi-Yau threefolds, and new topological transitions. (English) Zbl 1242.14038
This paper gives explicit constructions of “hyperconifolds”, which are discrete quotients of the conifold Calabi-Yau threefold. These varieties are singular, and they can ofter be resolved by both smoothing and crepant resolutions to obtain smooth compact Calabi-Yau manifolds which perform a geometric transition.

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
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