A duality in Buchsbaum rings and triangulated manifolds

Satoshi Murai, Isabella Novik, Ken Ichi Yoshida

研究成果: Article査読

6 被引用数 (Scopus)

抄録

Let Δ be a triangulated homology ball whose boundary complex is ∂Δ. A result of Hochster asserts that the canonical module of the Stanley–Reisner ring F[Δ] of Δ is isomorphic to the Stanley–Reisner module F[Δ, ∂Δ] of the pair (Δ, ∂Δ). This result implies that an Artinian reduction of F[Δ, ∂Δ] is (up to a shift in grading) isomorphic to the Matlis dual of the corresponding Artinian reduction of F[Δ]. We establish a generalization of this duality to all triangulations of connected orientable homology manifolds with boundary. We also provide an explicit algebraic interpretation of the hʺ-numbers of Buchsbaum complexes and use it to prove the monotonicity of hʺ-numbers for pairs of Buchsbaum complexes as well as the unimodality of hʺ-vectors of barycentric subdivisions of Buchsbaum polyhedral complexes. We close with applications to the algebraic manifold g-conjecture.

本文言語English
ページ(範囲)635-656
ページ数22
ジャーナルAlgebra and Number Theory
11
3
DOI
出版ステータスPublished - 2017
外部発表はい

ASJC Scopus subject areas

  • 代数と数論

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