The Lefschetz property for barycentric subdivisions of shellable complexes
نویسندگان
چکیده
منابع مشابه
The Lefschetz Property for Barycentric Subdivisions of Shellable Complexes
We show that an ’almost strong Lefschetz’ property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a CohenMacaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M -sequence. In particular, the (combinatorial) g-conjecture ...
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For a simplicial complex ∆ we study the effect of barycentric subdivision on ring theoretic invariants of its StanleyReisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke and Herzog & Srinivasan, that relates the multiplicity of a standard graded k-algebra to the product of the maximal shifts in its minimal free resolution up to the ...
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For a simplicial complex or more generally Boolean cell complex ∆ we study the behavior of the f and h-vector under barycentric subdivision. We show that if ∆ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney-Davis conjecture for spheres that are the subdivision of a Bool...
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Suppose a group G acts properly on a simplicial complex Γ . Let l be the number of G-invariant vertices, and p1,p2, . . . , pm be the sizes of the G-orbits having size greater than 1. Then Γ must be a subcomplex of Λ = Δl−1 ∗ ∂Δp1−1 ∗ · · · ∗ ∂Δpm−1. A result of Novik gives necessary conditions on the face numbers of Cohen–Macaulay subcomplexes of Λ. We show that these conditions are also suffi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2009
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-09-04794-1