Type changing, compact generalized Calabi--Yaus

We provide the first compact examples of type-changing generalized Calabi–Yau manifolds using Fei’s construction of non-Kähler Calabi–Yau manifolds on branched covers of twistor spaces \cite{Fei16}. The structure, which is generically of type 1 and changes to type 3, is constructed on the product of a hyperelliptic surface of genus three and a four-torus, ${\mathrm{\Sigma }}_3\times {\mathbb{T}}^4$, with starting point a non-Kähler Calabi–Yau structure.