Bimeromorphic geometry of LCK manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910454795730944 |
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| author | Ornea, Liviu Verbitsky, Misha |
| author_facet | Ornea, Liviu Verbitsky, Misha |
| contents | A locally conformally Kähler (LCK) manifold is a complex manifold $M$ which has a Kähler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the Kähler form is exact on the minimal Kähler cover of $M$. We prove that any bimeromorphic map $M'\rightarrow M$ is in fact holomorphic; in other words, $M$ has a unique minimal model. This can be applied to a wide class of LCK manifolds, such as the Hopf manifolds, their complex submanifolds and to OT manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03422 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bimeromorphic geometry of LCK manifolds Ornea, Liviu Verbitsky, Misha Differential Geometry Algebraic Geometry Complex Variables 32H04, 53C55 A locally conformally Kähler (LCK) manifold is a complex manifold $M$ which has a Kähler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the Kähler form is exact on the minimal Kähler cover of $M$. We prove that any bimeromorphic map $M'\rightarrow M$ is in fact holomorphic; in other words, $M$ has a unique minimal model. This can be applied to a wide class of LCK manifolds, such as the Hopf manifolds, their complex submanifolds and to OT manifolds. |
| title | Bimeromorphic geometry of LCK manifolds |
| topic | Differential Geometry Algebraic Geometry Complex Variables 32H04, 53C55 |
| url | https://arxiv.org/abs/2302.03422 |