On the module of differentials of order n of hypersurfaces

2018/08/06 by Barajas, Paul, Duarte, Daniel · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.02099

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.

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