## 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 |
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ページ（範囲） | 635-656 |

ページ数 | 22 |

ジャーナル | Algebra and Number Theory |

巻 | 11 |

号 | 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