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

TL;DR

This paper investigates the finite distance problem in the moduli space of non-Kähler Calabi--Yau threefolds using Hodge theory, extending existing criteria and exploring conditions for the $ ext{ extbackslash}partial ext{ extbackslash}bar{ extbackslash}partial$-lemma support.

Contribution

It extends C.-L. Wang's finite distance criterion to non-Kähler Calabi--Yau threefolds and provides new conditions for the $ ext{ extbackslash}partial ext{ extbackslash}bar{ extbackslash}partial$-lemma support in this setting.

Findings

Extended finite distance criterion to non-Kähler Calabi--Yau threefolds.

Provided sufficient conditions for $ ext{ extbackslash}partial ext{ extbackslash}bar{ extbackslash}partial$-lemma support.

Showed certain non-Kähler Calabi--Yau threefolds support the $ ext{ extbackslash}partial ext{ extbackslash}bar{ extbackslash}partial$-lemma.

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.