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arXiv · 2404.19125

Finite distance problem on the moduli of non-K\"{a}hler Calabi--Yau $\partial\bar{\partial}$-threefolds

Tsung-Ju Lee
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Abstract

In this article, we study the finite distance problem with respect to the period-map metric on the moduli of non-K\"{a}hler Calabi--Yau $\partial\bar{\partial}$-threefolds via Hodge theory. We extended C.-L. Wang's finite distance criterion for one-parameter degenerations to the present setting. As a byproduct, we also obtained a sufficient condition for a non-K\"{a}hler Calabi--Yau to support the $\partial\bar{\partial}$-lemma which generalizes the results by Friedman and Li. We also proved that the non-K\"{a}hler Calabi--Yau threefolds constructed by Hashimoto and Sano support the $\partial\bar{\partial}$-lemma.

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Tsung-Ju Lee. 2024-04-29. Finite distance problem on the moduli of non-K\"{a}hler Calabi--Yau $\partial\bar{\partial}$-threefolds. https://arxiv.org/abs/2404.19125

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