On splittings of deformations of pairs of complex structures and holomorphic vector bundles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911251213320192 |
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| author | Kasuya, Hisashi Purho, Valto |
| author_facet | Kasuya, Hisashi Purho, Valto |
| contents | We can show that the Kuranishi space of a pair $(M,E)$ of a compact Kähler manifold $M$ and its flat Hermitian vector bundle $E$ is isomorphic to the direct product of the Kuranishi space of $M$ and the Kuranishi space of $E$. We study non-Kähler case. We show that the Kuranishi space of a pair $(M,E)$ of a complex parallelizable nilmanifold $M$ and its trivial holomorphic vector bundle $E$ is isomorphic to the direct product of the Kuranishi space of $M$ and the Kuranishi space of $E$. We give examples of pairs $(M,E)$ of nilmanifolds $M$ with left-invariant abelian complex structures and their trivial holomorphic line bundles $E$ such that the Kuranishi spaces of pairs $(M,E)$ are not isomorphic to direct products of the Kuranishi spaces of $M$ and the Kuranishi spaces of $E$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On splittings of deformations of pairs of complex structures and holomorphic vector bundles Kasuya, Hisashi Purho, Valto Differential Geometry Algebraic Geometry Complex Variables We can show that the Kuranishi space of a pair $(M,E)$ of a compact Kähler manifold $M$ and its flat Hermitian vector bundle $E$ is isomorphic to the direct product of the Kuranishi space of $M$ and the Kuranishi space of $E$. We study non-Kähler case. We show that the Kuranishi space of a pair $(M,E)$ of a complex parallelizable nilmanifold $M$ and its trivial holomorphic vector bundle $E$ is isomorphic to the direct product of the Kuranishi space of $M$ and the Kuranishi space of $E$. We give examples of pairs $(M,E)$ of nilmanifolds $M$ with left-invariant abelian complex structures and their trivial holomorphic line bundles $E$ such that the Kuranishi spaces of pairs $(M,E)$ are not isomorphic to direct products of the Kuranishi spaces of $M$ and the Kuranishi spaces of $E$. |
| title | On splittings of deformations of pairs of complex structures and holomorphic vector bundles |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2511.04134 |