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

TL;DR

This paper constructs new solutions to the Hull-Strominger system by utilizing fibrations over singular K3 surfaces, expanding the class of manifolds known to admit such solutions with specific topological types.

Contribution

It introduces a novel method of using fibrations over K3 orbisurfaces to find smooth solutions to the Hull-Strominger system on new complex manifolds.

Findings

Constructed solutions on manifolds with specific topologies

Proved existence of complex structures with trivial canonical bundle

Extended known solutions to new classes of manifolds

Abstract

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