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Minimal Resolutions Over Codimension 2 Complete Intersections

David Eisenbud , $icon-email$ Irena Peeva

Abstract

We construct an explicit free resolution $T$ for a maximal Cohen-Macaulay module $M$ over a local complete intersection of codimension 2 with infinite residue field. The resolution is minimal when the module $M$ is a sufficiently high syzygy. Our starting point is a layered free resolution $L$ , described in [7], of length 2 over a regular local ring. We provide explicit formulas for the differential in $T$ in terms of the differential and homotopies on the finite resolution $L$ . One application of our construction is to describe Ulrich modules over a codimension 2 quadratic complete intersection.

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Minimal Resolutions Over Codimension 2 Complete Intersections

Abstract