Finite distance problem on the moduli of non-Kähler Calabi--Yau ∂∂-threefolds

2024/04/29 by Tsung-Ju Lee, Lee, Tsung-Ju
Mathematics · #14C30 (Secondary) #32Q25 (Primary) 32G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.19125

openalex publication_date 2024/04/29 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28

Abstract

In this article, we study the finite distance problem with respect to the period-map metric on the moduli of non-Kähler Calabi--Yau ∂∂-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 ∂∂-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 ∂∂-lemma.

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