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

Sz-Sheng Wang Yau Mathematical Sciences Center

Algebraic Geometry mathscidoc:1810.01002

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 \emph{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.
Calabi-yau, conifold transition
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@inproceedings{sz-shengon,
  title={On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions},
  author={Sz-Sheng Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181029160454339489165},
}
Sz-Sheng Wang. On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181029160454339489165.
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