Abstract |
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 analogously compute
the flag h-numbers hS and, by a change of variable formula, the cd-index. We
give an analogue of the Lefschetz operation for the cd-index. This
gives another proof of the non-negativity of the cd-index for complete fans.
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