# On the $k$-torsion of the module of differentials of order $n$ of hypersurfaces

## TL;DR

This paper characterizes when the module of differentials of order n of a hypersurface point is free of k-torsion, linking algebraic properties to the hypersurface's singularities.

## Contribution

It provides a new criterion for k-torsion freeness of higher-order differentials based on the singular locus of the local ring.

## Key findings

- k-torsion freeness is characterized by the singular locus
- The criterion applies to hypersurfaces at specific points
- Links algebraic differential properties to geometric singularities

## Abstract

We characterize the $k$-torsion freeness of the module of differentials of order $n$ of a point of a hypersurface in terms of the singular locus of the corresponding local ring.