2024/12/17 by Miyashita, Sora, Matteo Varbaro, Varbaro, Matteo · 2 citations
Mathematics · #13A02 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13H10 #Secondary 05E40
paper · pdf · doi:10.48550/arxiv.2412.12860
openalex publication_date 2024/12/17 · openalex created_date 2024/12/19 · openalex updated_date 2026/07/28
In this paper we prove that nearly Gorenstein Stanley-Reisner rings of dimension at least 3 are indeed Gorenstein. By previous work of the first author this yields a complete characterization of nearly Gorenstein Stanley-Reisner rings. We also show that a Cohen-Macaulay Stanley-Reisner ring is Gorenstein on the punctured spectrum if and only if either it is nearly Gorenstein or its canonical trace is the square of its irrelevant maximal ideal, and that the latter case happens exactly for non-orientable homology manifolds.