Examples of non-Kähler Calabi–Yau 3–folds with arbitrarily large b2

Abstract

We construct non-K\"{a}hler simply connected Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers by smoothing normal crossing varieties with trivial dualizing sheaves. We also give an example of a family of K3 surfaces with involutions which do not lift biregularly over the total space.