Partial normalizations of Coxeter arrangements and discriminants

Michel Granger (1) , David Mond (2) , Schulze Mathias (3)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 WMI - Warwick Mathematics Institute
3 OU - University of Oklahoma

We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin's Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We also describe an independent approach to these structures via duality of maximal Cohen-Macaulay fractional ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter group. Finally, we show that our partial normalizations give rise to new free divisors.

Mots clés: Coxeter group; logarithmic vector field; free divisor

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Michel Granger, David Mond, Schulze Mathias. Partial normalizations of Coxeter arrangements and discriminants. 2011. ⟨hal-00619215v1⟩