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arXiv · 2610.07826

Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families

Yinji Li·Mihai Păun·Zhiwei Wang·Xiangyu Zhou
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Abstract

Let $p:X\rightarrowΔ$ be a proper holomorphic submersion whose total space $X$ is a Kähler manifold. We prove that $\dim_{\mathbb C}H^0(X_t,mK_{X_t})$ is independent of $t$ for every integer $m\geq1$. This was conjectured by Y.-T. Siu in 2002.

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Yinji Li, Mihai Păun, Zhiwei Wang, Xiangyu Zhou. 2026-10-06. Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families. https://arxiv.org/abs/2610.07826

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