Michel Granger: Partial normalisations of Coxeter arrangements and discriminants

We study iin a work in common with Mond et M. Schultze a partial
normalisation of a Coxeter arrangement and of the discriminant in the
orbit space of the Coxeter reflection group. The ring structures of
these normalisation
arise from the structure of a Frobenius variety on the orbit space and
from a lifting (without unit) to the space of the arangement itself.
We give also another description of these structures in terms of a
duality realising an involution on the set of maximal Cohen Macaulay
fractionnal ideals. This leads to a differential condition of order 3
between the Coxeter invariants Using these rings we are also able to
build new examples of free divisors (in the sense of K. Saito) by the
mean of an adjunction type process.