A Complex Structure on $T^2\times S^4$: The Genus-One Case of Calabi's Problem

Abstract

We construct a complex structure on $T^2\times S^4$, giving an affirmative answer to the genus-one case of Calabi's problem. The resulting compact complex threefold is non-Kähler and admits no biholomorphic product decomposition.

arXiv comment31 pages