Aspects of deformation invariance of plurigenera of Kähler varieties
Abstract
We study several aspects of deformation invariance of plurigenera in Kähler families over a smooth curve. First, for a relatively flat coherent sheaf, we characterize local constancy of fiberwise cohomology dimension by equivalent conditions in terms of extension, base change, torsion freeness of higher direct images, and the vanishing of jumping classes. Then, combining this criterion with the Kähler minimal model program, we prove invariance of plurigenera for Kähler families of threefolds whose central fiber has canonical singularities, and for smooth Kähler families of maximal Albanese dimension. We also establish deformation invariance of log plurigenera when the central fiber is projective, and is of log general type. We prove the invariance of higher cohomological plurigenera assuming that the canonical bundle of the total space is semipositive. Finally, we extend Z.~Li--Z.~Wang's deformation invariance result for generalized polarized pairs with abundant nef parts from projective families to Moishezon families.
Related
- Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families
- Invariance of plurigenera for Kähler families with nef canonical bundles
- Invariance of logarithmic plurigenera and adjoint volumes in Kähler families
- Deformation invariance of canonical nefness in smooth Kahler morphisms
- Kähler-Ricci Flow is Symplectic Deflation plus an Exact Symplectic Deformation
BibTeX
@misc{feng2026aspects,
title = {{Aspects of deformation invariance of plurigenera of Kähler varieties}},
author = {Jiawei Feng and Yi Li and Sheng Rao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17817},
eprint = {2610.17817},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17817},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Aspects of deformation invariance of plurigenera of Kähler varieties
AU - Jiawei Feng
AU - Yi Li
AU - Sheng Rao
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17817
UR - https://arxiv.org/abs/2610.17817
AB - We study several aspects of deformation invariance of plurigenera in Kähler families over a smooth curve. First, for a relatively flat coherent sheaf, we characterize local constancy of fiberwise cohomology dimension by equivalent conditions in terms of extension, base change, torsion freeness of higher direct images, and the vanishing of jumping classes. Then, combining this criterion with the Kähler minimal model program, we prove invariance of plurigenera for Kähler families of threefolds whose central fiber has canonical singularities, and for smooth Kähler families of maximal Albanese dimension. We also establish deformation invariance of log plurigenera when the central fiber is projective, and is of log general type. We prove the invariance of higher cohomological plurigenera assuming that the canonical bundle of the total space is semipositive. Finally, we extend Z.~Li--Z.~Wang's deformation invariance result for generalized polarized pairs with abundant nef parts from projective families to Moishezon families.
ER -