Finite distance problem on the moduli of non-Kähler Calabi--Yau $\partial\bar{\partial}$-threefolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909185220804608 |
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| author | Lee, Tsung-Ju |
| author_facet | Lee, Tsung-Ju |
| contents | In this article, we study the finite distance problem with respect to the period-map metric on the moduli of non-Kähler 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-Kähler Calabi--Yau to support the $\partial\bar{\partial}$-lemma which generalizes the results by Friedman and Li. We also proved that the non-Kähler Calabi--Yau threefolds constructed by Hashimoto and Sano support the $\partial\bar{\partial}$-lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite distance problem on the moduli of non-Kähler Calabi--Yau $\partial\bar{\partial}$-threefolds Lee, Tsung-Ju Algebraic Geometry 32Q25 (Primary) 32G05, 14C30 (Secondary) In this article, we study the finite distance problem with respect to the period-map metric on the moduli of non-Kähler 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-Kähler Calabi--Yau to support the $\partial\bar{\partial}$-lemma which generalizes the results by Friedman and Li. We also proved that the non-Kähler Calabi--Yau threefolds constructed by Hashimoto and Sano support the $\partial\bar{\partial}$-lemma. |
| title | Finite distance problem on the moduli of non-Kähler Calabi--Yau $\partial\bar{\partial}$-threefolds |
| topic | Algebraic Geometry 32Q25 (Primary) 32G05, 14C30 (Secondary) |
| url | https://arxiv.org/abs/2404.19125 |