Holomorphic one-forms without zeros on K\"ahler manifolds of Kodaira codimension one
We give a bimeromorphic classification of compact K\"ahler manifolds of Kodaira codimension one that admit a holomorphic one form without zeros.
math.CV↗
arXiv subjects
Simon Pietig
Publications and source records attributed to Simon Pietig.
Holomorphic 1-forms without zeros on K\"ahler threefolds
We classify all smooth compact connected K\"ahler threefolds that admit the structure of a $C^\infty$-fiber bundle over the circle. This generalizes the work of Hao and Schreieder in the projective case. In contrast to the projective case, there cannot always exist a smooth morphism to a positive-dimensional torus. Instead, we show that such a compact K\"ahler threefold admits a finite \'etale cover that is bimeromorphic to a $\mathbb{P}^1$-, $\mathbb{P}^2$-, or Hirzebruch surface-bundle over a locally trivial torus-fiber bundle over a smooth compact connected K\"ahler base. Our results prove Kotschick's conjecture in dimension 3.
math.AG↗