Year: 2025
Type: preprint
Abstract: We classify all smooth compact connected Kähler 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 Kähler threefold admits a finite étale 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 Kähler base. Our results prove Kotschick's conjecture in dimension 3.
Source: arXiv (Cornell University)
Author: Pietig, Simon
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416261046
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