Translator Disclaimer
2017 A duality in Buchsbaum rings and triangulated manifolds
Satoshi Murai, Isabella Novik, Ken-ichi Yoshida
Algebra Number Theory 11(3): 635-656 (2017). DOI: 10.2140/ant.2017.11.635

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 h-numbers of Buchsbaum complexes and use it to prove the monotonicity of h-numbers for pairs of Buchsbaum complexes as well as the unimodality of h-vectors of barycentric subdivisions of Buchsbaum polyhedral complexes. We close with applications to the algebraic manifold g-conjecture.

Citation

Download Citation

Satoshi Murai. Isabella Novik. Ken-ichi Yoshida. "A duality in Buchsbaum rings and triangulated manifolds." Algebra Number Theory 11 (3) 635 - 656, 2017. https://doi.org/10.2140/ant.2017.11.635

Information

Received: 8 March 2016; Accepted: 8 October 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1370.13019
MathSciNet: MR3649363
Digital Object Identifier: 10.2140/ant.2017.11.635

Subjects:
Primary: 13F55
Secondary: 05E40, 13H10, 52B05, 57Q15

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 3 • 2017
MSP
Back to Top