Holomorphic 1-forms without zeros on Kähler threefolds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915361488633856 |
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| author | Pietig, Simon |
| author_facet | Pietig, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Holomorphic 1-forms without zeros on Kähler threefolds Pietig, Simon Algebraic Geometry Complex Variables Geometric Topology 32Q55, 32Q15, 32J17 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. |
| title | Holomorphic 1-forms without zeros on Kähler threefolds |
| topic | Algebraic Geometry Complex Variables Geometric Topology 32Q55, 32Q15, 32J17 |
| url | https://arxiv.org/abs/2506.22067 |