Mirror Symmetry,Tyurin Degenerations,and Calabi-Yau Fibrations

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  In 2002,at the Fano Conference,Andrey Tyurin made two insightful proposals regarding Calabi-Yau manifolds and their moduli:(1)a definition of “constructive” Calabi-Yau manifolds,i.e.,those which admit degenerations to a union of two quasi-Fano varieties intersecting transversely,and(2)a question of how the mirror Calabi-Yau manifolds should be related to the mirror Landau-Ginzburg models of the component Fano varieties.
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