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Combinatorial intersection cohomology for fans

Combinatorial intersection cohomology for fans

We investigate minimal extension sheaves on arbitrary (possibly non-rational) fans as an approach toward a combinatorial "virtual'' intersection cohomology. These are flabby sheaves of graded modules over a sheaf of polynomial rings, satisfying three relatively simple axioms that characterize the equivariant intersection cohomology sheaves on toric varieties. As in "classical'' …