### Abstract

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.

Original language | English |
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Pages (from-to) | 635-656 |

Number of pages | 22 |

Journal | Algebra and Number Theory |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

Externally published | Yes |

### Keywords

- Buchsbaum rings
- H-vectors
- Stanley–Reisner rings
- Triangulated manifolds

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Algebra and Number Theory*,

*11*(3), 635-656. https://doi.org/10.2140/ant.2017.11.635