Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 3 (2017), 635-656.
A duality in Buchsbaum rings and triangulated manifolds
Let be a triangulated homology ball whose boundary complex is . A result of Hochster asserts that the canonical module of the Stanley–Reisner ring of is isomorphic to the Stanley–Reisner module of the pair . This result implies that an Artinian reduction of is (up to a shift in grading) isomorphic to the Matlis dual of the corresponding Artinian reduction of . 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 -numbers of Buchsbaum complexes and use it to prove the monotonicity of -numbers for pairs of Buchsbaum complexes as well as the unimodality of -vectors of barycentric subdivisions of Buchsbaum polyhedral complexes. We close with applications to the algebraic manifold -conjecture.
Algebra Number Theory, Volume 11, Number 3 (2017), 635-656.
Received: 8 March 2016
Accepted: 8 October 2016
First available in Project Euclid: 19 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 05E40: Combinatorial aspects of commutative algebra 52B05: Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx] 57Q15: Triangulating manifolds
Murai, Satoshi; Novik, Isabella; Yoshida, Ken-ichi. A duality in Buchsbaum rings and triangulated manifolds. Algebra Number Theory 11 (2017), no. 3, 635--656. doi:10.2140/ant.2017.11.635. https://projecteuclid.org/euclid.ant/1508431775