Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Feng, Jiawei, Li, Yi, Rao, Sheng
Institution: Wuhan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221817348