Towards a combinatorial Intersection Cohomology for Fans

Details Towards a combinatorial Intersection Cohomology for Fans Towards a combinatorial Intersection Cohomology for Fans

2000-02-22

arxiv.org/abs/math/0002178v2

Mathematics

Algebraic Geometry

8 pages, TeX, special macros are included, To appear in CRAS, Acad. Sci. Paris

Scientific paper

10.1016/S0764-4442(00)00149-X

The real intersection cohomology of a toric variety is described in a purely combinatorial way using methods of elementary commutative algebra only. We define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the fan as an axiomatic characterization of the equivariant intersection cohomology sheaf. This provides a purely algebraic interpretation of Stanley's generalized f- and g-vector of an arbitrary polytope or complete fan under a natural vanishing condition. -- The results presented in this note originate from joint work with G.Barthel, J.-P.Brasselet and L.Kaup, continuing earlier research (see math.AG/9904159). A detailed exposition will appear elsewhere (see math.AG/0002181).

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