Type: Article

On the module of differentials of order n of hypersurfaces

Barajas Paul; Duarte, Daniel.;

Abstract:

We give an explicit presentation of the module of differentials of order n of a finitely generated algebra via a higher-order Jacobian matrix. We use the presentation to study some aspects of this module in the case of hypersurfaces. More precisely, we prove higher-order versions of known results relating freness and torsion-freness of the module of differentials with the regularity and normality of the hypersurface. We also study its projective dimension.