Fibrations Over Singular K3 Surfaces and New Solutions to the Hull-Strominger System

Using fibrations over K3 orbisurfaces we construct new smooth solutions to the Hull-Strominger system. In particular, we prove that, for $4\le k\le 22$ and $5\le r\le 22$, the smooth manifolds $S^1\times {\mathrm{♯}}_k(S^2\times S^3)$ and ${\mathrm{♯}}_r(S^2\times S^4){\mathrm{♯}}_{r+1}(S^3\times S^3)$, have a complex structure with trivial canonical bundle and admit a solution to the Hull-Strominger system.