A remark on extension of log-pluricanononical forms for nondegenerate hypersurfaces

TL;DR

This paper characterizes log-pluricanonical forms on nondegenerate hypersurfaces and demonstrates their extendability to deformations, enabling a unified approach to log-canonical models in algebraic geometry.

Contribution

It extends previous work by explicitly describing log-pluricanonical forms and their extendability to deformations for nondegenerate hypersurfaces.

Findings

Log-pluricanonical forms are extendable to 1-parameter deformations.

Equisingular deformations admit a simultaneous log-canonical model.

Provides a complement to Marcel Morales's earlier results.

Abstract

We determine, complementing a paper by Marcel Morales, the log-pluricanonical forms on a nondegenerate hypersurface. This description shows that they are extendable to 1-parameter deformations. For an equisingular deformation we thus obtain a simultaneous log-canonical model.