# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1906.08321