On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions

Sz-Sheng Wang

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arXiv · 1603.03929

On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions

Sz-Sheng Wang

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Abstract

We supply a detailed proof of the result by P.S. Green and T. H$\ddot{\text{u}}$bsch that all complete intersection Calabi--Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the standard web). We also introduce a subclass of small transitions which we call primitive small transitions and study such subclass. More precisely, given a small projective resolution $\pi : \widehat{X} \rightarrow X$ of a Calabi--Yau 3-fold $X$, we show that if the natural closed immersion $Def(\widehat{X}) \hookrightarrow Def(X)$ is an isomorphism then $X$ has only ODPs as singularities.

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Sz-Sheng Wang. 2016-03-12. On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions. https://arxiv.org/abs/1603.03929

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