On the module of differentials of order n of hypersurfaces

Abstract

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