The cd-index of fans and posets
نویسندگان
چکیده
منابع مشابه
The cd -index of fans and posets
The number of flags in a complete fan, or more generally in an Eulerian poset, is encoded in the cd-index. We prove the non-negativity of the cd-index for complete fans, regular CW -spheres and Gorenstein* posets.
متن کاملThe Cd-index of Fans and Lattices
where hk = dim(A(∆)⊗AR) k. When the fan ∆ is rational, it corresponds to a toric variety X(∆) and the numbers hk are the even betti numbers of the cohomology of X(∆). In any case, they satisfy the Poincaré duality hk = hn−k. When the fan ∆ is complete but not necessarily simplicial, one can apply the same construction to the first barycentric subdivision B(∆) of ∆. We can label a 1-dimensional ...
متن کاملLefschetz decomposition and the cd-index of fans
The goal of this article is to give a Lefschetz type decomposition for the cd-index of a complete fan. To a complete simplicial fan one can associate a toric variety X, the even Betti numbers hi of X and the numbers gi = hi − hi−1. If the fan is projective, then non-negativity of gi follows from the Lefschetz decomposition of the cohomology. In the case of a nonsimplicial complete fan, one can ...
متن کاملDecomposition theorem for the cd-index of Gorenstein* posets
We prove a decomposition theorem for the cd-index of a Gorenstein* poset analogous to the decomposition theorem for the intersection cohomology of a toric variety. From this we settle a conjecture of Stanley that the cd-index of Gorenstein* lattices is minimized on Boolean algebras.
متن کامل9 S ep 2 00 5 LEFSCHETZ DECOMPOSITION AND THE CD - INDEX OF FANS
The goal of this article is to give a Lefschetz type decomposition for the cd-index of a complete fan. To a complete simplicial fan one can associate a toric variety X, the even Betti numbers hi of X and the numbers gi = hi − hi−1. If the fan is projective, then non-negativity of gi follows from the Lefschetz decomposition of the cohomology. In the case of a nonsiplicial complete fan one can an...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2006
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x06001928