Title: Partial normalization of Coxeter arrangements
Abstract: In a recent paper in common with D. Mond and M. Schultze we
define partial normalizations of Coxeter arrangements and of their
discriminants. We shall begin with elementary examples like A3 et B3 ,
and then recall the classification of irreducible Coxeter
arrangements, Chevalley's theorem about the ring of invariants
polynomial and finally the notion of a free divisor in the sense of
Saito. Coxeter arrangements and their discriminants are a well known
example of such divisors. We will show how natural are the structural
rings of the normalisations cited above. We shall conclude by giving
an idea of the proof which relies on the existence of a structure of a
Frobenius variety on the discriminant and we shall consider other
natural situations where such a partial normalization might appear.