A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System

Abstract

We propose a new construction of compact non-Kähler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on $\hat{I}{\pounds }_g\times T^4$, where $\hat{I}{\pounds }_g$ is an immersed minimal surface of genus $g\ge 3$ in $T^3$.

17 pages, comments are welcome! Updates in v2: small revisions with new references added