Cohen–Macaulayness and canonical module of residual intersections
Résumé
We show the Cohen-Macaulayness and describe the canonical module of residual intersections J = a : R I in a Cohen-Macaulay local ring R, under sliding depth type hypotheses. For this purpose, we construct and study, using a recent article of Hassanzadeh and the second author, a family of complexes that contains important information on a residual intersection and its canonical module. We also determine several invariants of residual intersections as the graded canonical module, the Hilbert series, the Castelnuovo-Mumford regularity and the type. Finally, whenever I is strongly Cohen-Macaulay, we show duality results for residual intersections that are closely connected to results by Eisenbud and Ulrich. It establishes some tight relations between the Hilbert series of some symmetric powers of I/a. We also provide closed formulas for the types and for the Bass numbers of some symmetric powers of I/a.
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