The resolution of the generic residual intersection of a complete intersection
In the theory of linkage Peskine and Szpiro produced a resolution of one ideal of a pair of linked ideals in terms of the resolution of the other ideal and a Koszul complex. Since the concept of residual intersection, introduced by Artin and Nagata, is a generalization of the linkage the authors pose the problem of an analogous result: If \(J\) is the residual intersection of an ideal \(I\) with respect to an ideal generated by elements \(z_1,\ldots,z_m\), then one wants to express the resolution of \(J\) in terms of the resolution of \(I\) and the Koszul complex on \(z_1,\ldots,z_m\). In this paper one resolves \(J\) in the case that \(I\) is a complete intersection and the \(z_j\) are generic linear combinations of the generators of \(I\). The first section is a review of multilinear algebra, followed by definitions of the main constituents of the resolution. Preliminary acyclicity results are given in section 2, while the resolution itself may be found in section 3. The final section 4 contains a discussion of the generic case, with applications to residual intersection and canonical modules.
scientific article; zbMATH DE number 4139909
scientific article