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Invariance of plurigenera for Kähler families with nef canonical bundles
Abstract
Let p:X→Δ be a proper holomorphic submersion from a Kähler manifold X. We prove that, if KXt is nef for every t∈Δ, then dimℂH0(Xt,mKXt) is independent of t for every integer m≥1. This gives a partial answer to Siu's conjecture on the invariance of plurigenera for Kähler families.
Related
- Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families
- Invariance of logarithmic plurigenera and adjoint volumes in Kähler families
- Aspects of deformation invariance of plurigenera of Kähler varieties
- Deformation invariance of canonical nefness in smooth Kahler morphisms
- Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
BibTeX
@misc{deng2026invariance,
title = {{Invariance of plurigenera for Kähler families with nef canonical bundles}},
author = {Fusheng Deng and Jiafu Ning and Zhiwei Wang and Xiangyu Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37804},
eprint = {2609.37804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37804},
}
RIS
TY - UNPB
TI - Invariance of plurigenera for Kähler families with nef canonical bundles
AU - Fusheng Deng
AU - Jiafu Ning
AU - Zhiwei Wang
AU - Xiangyu Zhou
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37804
UR - https://arxiv.org/abs/2609.37804
AB - Let p:X→Δ be a proper holomorphic submersion from a Kähler manifold X. We prove that, if K_X_t is nef for every t∈Δ, then dim_ℂH^0(X_t,mK_X_t) is independent of t for every integer m≥1. This gives a partial answer to Siu's conjecture on the invariance of plurigenera for Kähler families.
ER -