K\"{a}hler structures for holomorphic submersions

Chi Li

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arXiv · 2302.07220

K\"{a}hler structures for holomorphic submersions

Chi Li

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Abstract

In this short paper, for any holomorphic submersion $\pi: X\rightarrow B$, we derive a criterion for $X$ to have K\"{a}hler structures. This criterion generalizes Blanchard's criterion for a special class of isotrivial holomorphic submersions. We use this criterion to answer a question of Harvey-Lawson in the case of fiber dimension one. As the main application, we prove that the existence of Hermitian-Symplectic structures on certain class of holomorphic submersions with K\"{a}hler fibers and K\"{a}hler bases implies that the total spaces are K\"{a}hler. This class includes isotrivial submersions and torus fibrations.

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Chi Li. 2023-02-14. K\"{a}hler structures for holomorphic submersions. https://arxiv.org/abs/2302.07220

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