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Delphine PolŽ (–kŠC“¹‘åŠwCJSPS)
On a generalization of Solomon Terao formula
Abstract:
The characteristic polynomial of a subspace arrangement is
an important combinatorial invariant which carries information about
the combinatorics and the topology of the arrangement and its
complement. The Solomon-Terao formula gives the relation between the
characteristic polynomial of an hyperplane arrangement and the
Hilbert-Poincaré series of the modules of logarithmic differential
forms. We will study in this talk a generalization of this formula for
equidimensional subspace arrangements of higher codimension. The
generalized Solomon-Terao formula is satisfied by all line
arrangements, but we will give examples showing that it may not be
satisfied by some higher dimensional subspace arrangements.