Zeros of one-forms and homologically trivial fibrations
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915691772248064 |
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| author | Schreieder, Stefan Yang, Ruijie |
| author_facet | Schreieder, Stefan Yang, Ruijie |
| contents | We show that a conjecture of Kotschick about one-forms without zeros on compact Kähler manifolds follows in the case of simple Albanese torus from a conjecture of Bobadilla and Kollár about homologically trivial fibrations. As an application, we prove Kotschick's conjecture for compact Kähler manifolds X whose first betti number is at least 2dim(X)-2 and Albanese torus is simple. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_05697 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Zeros of one-forms and homologically trivial fibrations Schreieder, Stefan Yang, Ruijie Algebraic Geometry Differential Geometry 14F45, 32Q55, 32S60 We show that a conjecture of Kotschick about one-forms without zeros on compact Kähler manifolds follows in the case of simple Albanese torus from a conjecture of Bobadilla and Kollár about homologically trivial fibrations. As an application, we prove Kotschick's conjecture for compact Kähler manifolds X whose first betti number is at least 2dim(X)-2 and Albanese torus is simple. |
| title | Zeros of one-forms and homologically trivial fibrations |
| topic | Algebraic Geometry Differential Geometry 14F45, 32Q55, 32S60 |
| url | https://arxiv.org/abs/2210.05697 |