A duality in Buchsbaum rings and triangulated manifolds

作者：Murai Satoshi^*; Novik Isabella; Yoshida Ken ichi

来源：Algebra and Number Theory, 2017, 11(3): 635-656.

DOI：10.2140/ant.2017.11.635

• triangulated manifolds
• Buchsbaum rings
• h-vectors
• Stanley-Reisner rings

Let 1 be a triangulated homology ball whose boundary complex is partial derivative Delta. A result of Hochster asserts that the canonical module of the Stanley-Reisner ring F[Delta] of Delta is isomorphic to the Stanley-Reisner module F[Delta, partial derivative Delta] of the pair (Delta, partial derivative Delta]. This result implies that an Artinian reduction of F[Delta, partial derivative Delta] is (up to a shift in grading) isomorphic to the Matlis dual of the corresponding Artinian reduction of F[Delta]. 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.

• 出版日期2017