A duality in Buchsbaum rings and triangulated manifolds

Satoshi Murai, Isabella Novik, Ken Ichi Yoshida

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)635-656
Number of pages22
JournalAlgebra and Number Theory
Volume11
Issue number3
DOIs
Publication statusPublished - 2017 Jan 1
Externally publishedYes

Fingerprint

Duality
Ring
Homology
Isomorphic
Barycentric Subdivision
Use of numbers
Canonical Module
G-manifolds
H-vector
Unimodality
Manifolds with Boundary
Grading
Triangulation
Monotonicity
Ball
Imply
Module

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

A duality in Buchsbaum rings and triangulated manifolds. / Murai, Satoshi; Novik, Isabella; Yoshida, Ken Ichi.

In: Algebra and Number Theory, Vol. 11, No. 3, 01.01.2017, p. 635-656.

Research output: Contribution to journalArticle

Murai, Satoshi ; Novik, Isabella ; Yoshida, Ken Ichi. / A duality in Buchsbaum rings and triangulated manifolds. In: Algebra and Number Theory. 2017 ; Vol. 11, No. 3. pp. 635-656.
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