Minimal Resolutions Over Codimension 2 Complete Intersections

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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Funding

The work on this paper profited from the good conditions for mathematics at MSRI, and was partially supported by the National Science Foundation under Grant 0932078000. The authors received partial support under the National Science Foundation Grants DMS-1502190, DMS-1702125, and DMS-1406062.

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Correspondence to Irena Peeva.

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Eisenbud, D., Peeva, I. Minimal Resolutions Over Codimension 2 Complete Intersections. Acta Math Vietnam 44, 141–157 (2019). https://doi.org/10.1007/s40306-018-0293-9

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Keywords

  • Free resolutions
  • Complete intersections
  • CI operators
  • Eisenbud operators
  • Maximal Cohen-Macaulay modules

Mathematics Subject Classification (2010)

  • Primary 13D02