A classification of nearly Gorenstein monomial ideals

Abstract

We classify nearly Gorenstein monomial ideals over an arbitrary field. In dimension zero, we compute the canonical trace ideal using a graph on the socle monomials. In positive dimension, we prove a dimension bound under unmixedness and a connectedness condition, with weaker assumptions on the canonical trace ideal.

arXiv comment16 pages. Substantially revised, with a new title. The nearly Gorenstein classification has been extended to arbitrary monomial ideals