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arXiv · 2511.04134

On splittings of deformations of pairs of complex structures and holomorphic vector bundles

Hisashi Kasuya·Valto Purho
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Abstract

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 $E$.

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Hisashi Kasuya, Valto Purho. 2025-11-06. On splittings of deformations of pairs of complex structures and holomorphic vector bundles. https://arxiv.org/abs/2511.04134

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