Ring structure, uniform expressions and intersection homology

Details Ring structure, uniform expressions and intersection homology Ring structure, uniform expressions and intersection homology

1998-05-22

arxiv.org/abs/math/9805100v1

Mathematics

Algebraic Geometry

15 pages. LaTeX

Scientific paper

Although intersection homology lacks a ring structure, certain expressions (called uniform) in the intersection homology of an irreducible projective variety $X$ always give the same value, when computed via the decomposition theorem on any resolution $X_r\to X$. This paper uses uniform (and non-uniform) expressions to define what is believed to be the usual intersection homology (and its local-global variant) of a convex polytope (or a projective toric variety). Such expressions are generated by the facets, and so may lead to necessary numerical conditions on the flag vector. Most of the concepts, however, apply to more general algebraic varieties, and perhaps some other situations also.

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