Examples of non-K\"ahler Calabi-Yau manifolds with arbitrarily large $b_2$

TL;DR

This paper constructs non-Kähler Calabi-Yau manifolds of dimension four or higher with arbitrarily large second Betti numbers, using smoothing techniques on normal crossing varieties, revealing new geometric structures with K3 fibrations.

Contribution

It introduces a method to produce non-Kähler Calabi-Yau manifolds with large second Betti numbers via smoothing normal crossing varieties, expanding known examples.

Findings

Existence of non-Kähler Calabi-Yau manifolds with arbitrarily large b_2

Construction involves smoothing normal crossing varieties

Manifolds have K3 fibrations over smooth projective bases

Abstract

We construct non-K\"ahler Calabi-Yau manifolds of dimension $\ge$ 4 with arbitrarily large 2nd Betti numbers by smoothing normal crossing varieties. The examples have K3 fibrations over smooth projective varieties and their algebraic dimensions are of codimension 2.