Conormal Modules via Primitive Ideals,

The main object of this note is to study the conormal module M and the computation of the second symbolic power (2) of an ideal in the residue ring / of a polynomial ring over a field of characteristic zero. The torsion part T(M) of M and the torsion free module M/T(M) are expressed by the primitive ideal of relative to . Two characterizations for M/T(M) to be free are proved. Some immediate applications are worked out.