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April 2016 Buchstaber invariant, minimal non-simplices and related
Anton Ayzenberg
Osaka J. Math. 53(2): 377-395 (April 2016).


Buchstaber invariant is a numerical characteristic of a simplicial complex (or a polytope), measuring the degree of freeness of the torus action on the corresponding moment-angle complex. Recently an interesting combinatorial theory emerged around this invariant. In this paper we answer two questions, considered as conjectures in [2], [11]. First, Buchstaber invariant of a convex polytope $P$ equals $1$ if and only if $P$ is a pyramid. Second, there exist two simplicial complexes with isomorphic bigraded $\mathrm{Tor}$-algebras, which have different Buchstaber invariants. In the proofs of both statements we essentially use the result of N. Erokhovets, relating Buchstaber invariant of simplicial complex $K$ to the distribution of minimal non-simplices of $K$. Gale duality is used in the proof of the first statement. Taylor resolution of a Stanley--Reisner ring is used for the second.


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Anton Ayzenberg. "Buchstaber invariant, minimal non-simplices and related." Osaka J. Math. 53 (2) 377 - 395, April 2016.


Published: April 2016
First available in Project Euclid: 27 April 2016

zbMATH: 1339.05439
MathSciNet: MR3492804

Primary: 05C15 , 05E45 , 13D02 , 13F55 , 52B11 , 52B35 , 57S25

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics


Vol.53 • No. 2 • April 2016
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