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A minimal free resolution of the duplication of a monomial ideal

  • Carlos E. Valencia,
  • David C. Molano,
  • Javier A. Moreno

摘要

This article explores a novel operation of a monomial ideal, termed duplication, which produces a monomial ideal \(I^\diamond \) I from another I. This operation is inspired by and generalizes how vertex duplication affects the edge ideal of a graph. The main result describes a multigraded minimal free resolution of \(I^\diamond \) I as long as we know a resolution for I. Consequently, we obtain formulas for the projective dimension and depth of \(I^\diamond \) I in terms of the corresponding invariants of I.