Construction of non-K\"ahler Calabi-Yau manifolds by log deformations

TL;DR

This paper surveys recent methods for constructing non-Kähler Calabi-Yau manifolds through smoothing techniques involving SNC varieties and automorphisms, introducing a new example from abelian surface automorphisms.

Contribution

It provides a comprehensive survey of recent construction techniques and introduces a novel example of non-Kähler Calabi-Yau manifold from abelian surface automorphisms.

Findings

Survey of recent construction methods for non-Kähler Calabi-Yau manifolds

Introduction of a new example via smoothing an SNC 3-fold from abelian surface automorphisms

Identification of non-trivial isomorphisms in the construction process

Abstract

We survey recent construction of non-K\"ahler Calabi-Yau manifolds by smoothing SNC varieties obtained by non-trivial isomorphisms of strict Calabi-Yau manifolds. We also give a new example by smoothing an SNC 3-fold which are constructed from automorphisms of an abelian surface.