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Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families
Abstract
Let p:X→Δ be a proper holomorphic submersion whose total space X is a Kähler manifold. We prove that dimℂH0(Xt,mKXt) is independent of t for every integer m≥1. This was conjectured by Y.-T. Siu in 2002.
Related
- Invariance of plurigenera for Kähler families with nef canonical bundles
- Invariance of logarithmic plurigenera and adjoint volumes in Kähler families
- Aspects of deformation invariance of plurigenera of Kähler varieties
- Du Bois cohomology of noncommutative spaces and the Hodge numbers invariance conjecture for singular varieties
- Partition invariance of variation indices and classical p-variation spaces
BibTeX
@misc{li2026variation,
title = {{Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families}},
author = {Yinji Li and Mihai Păun and Zhiwei Wang and Xiangyu Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07826},
eprint = {2610.07826},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07826},
}
RIS
TY - UNPB
TI - Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families
AU - Yinji Li
AU - Mihai Păun
AU - Zhiwei Wang
AU - Xiangyu Zhou
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07826
UR - https://arxiv.org/abs/2610.07826
AB - Let p:X→Δ be a proper holomorphic submersion whose total space X is a Kähler manifold. We prove that dim_ℂH^0(X_t,mK_X_t) is independent of t for every integer m≥1. This was conjectured by Y.-T. Siu in 2002.
ER -