The twistor space of a compact hypercomplex manifold is never Moishezon
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910679383932928 |
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| author | Gorginyan, Yulia |
| author_facet | Gorginyan, Yulia |
| contents | Let (X,I,J,K) be a compact hypercomplex manifold, i.e. a smooth manifold X with an action of the quaternion algebra (Id,I,J,K) on the tangent bundle TX, inducing integrable almost complex structures. For any $(a, b, c) \in S^2$, the linear combination $L := aI + bJ + cK$ defines another complex structure on X. This results in a $C P^1$-family of complex structures called the twistor family. Its total space is called the twistor space. We show that the twistor space of a compact hypercomplex manifold is never Moishezon and, moreover, it is never Fujiki class C (in particular, never Kahler and never projective). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The twistor space of a compact hypercomplex manifold is never Moishezon Gorginyan, Yulia Algebraic Geometry Differential Geometry Let (X,I,J,K) be a compact hypercomplex manifold, i.e. a smooth manifold X with an action of the quaternion algebra (Id,I,J,K) on the tangent bundle TX, inducing integrable almost complex structures. For any $(a, b, c) \in S^2$, the linear combination $L := aI + bJ + cK$ defines another complex structure on X. This results in a $C P^1$-family of complex structures called the twistor family. Its total space is called the twistor space. We show that the twistor space of a compact hypercomplex manifold is never Moishezon and, moreover, it is never Fujiki class C (in particular, never Kahler and never projective). |
| title | The twistor space of a compact hypercomplex manifold is never Moishezon |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2410.24085 |