English

Invariance of plurigenera and good minimal models

Algebraic Geometry 2025-06-30 v2

Abstract

Nakayama showed that deformation invariance of plurigenera for smooth complex varieties follows from the MMP and Abundance Conjectures. We generalize his result to families of singular pairs over DVRs of positive or mixed characteristic. As an application we show invariance of plurigenera for deformations of good minimal models of general type varieties whose canonical model has rational singularities as well as boundedness of Gorenstein canonical models of dimension three and fixed volume over an algebraically closed field of characteristic p>5p>5.

Keywords

Cite

@article{arxiv.2207.08107,
  title  = {Invariance of plurigenera and good minimal models},
  author = {Iacopo Brivio},
  journal= {arXiv preprint arXiv:2207.08107},
  year   = {2025}
}

Comments

37 pages, title changed, improved exposition, strengthened results. New example of failure of invariance of plurigenera added. Comments welcome