Conormal modules via Primitive ideals

Abstract

The main object of this note is to study the conormal module $M$ and the computation of the second symbolic power ${\bar{I}}^{(2)}$ of an ideal $\bar{I}$ in the residue ring $R/H$ of a polynomial ring $R$ 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 $I$ relative to $H$. Two characterizations for $M/T(M)$ to be free are proved. Some immediate applications are worked out.

11 pages, Latex2e file