On a representation of the fundamental class of an ideal due to Lejeune-Jalabert

Abstract

Lejeune-Jalabert showed that the fundamental class of a Cohen-Macaulay ideal $\mathfrak{a}\subset {\mathcal{O}}_0$ admits a representation as a residue, constructed from a free resolution of $\mathfrak{a}$, multiplied by a certain differential form coming from the resolution. We give an explicit description of this differential form in the case where the free resolution is the Scarf resolution of a generic monomial ideal. As a consequence we get a new proof and a refinement of Lejeune-Jalabert's result in this case.

arXiv comment20 pages