Finite Groups of Essential Dimension 2

We classify all finite groups of essential dimension 2 over an algebraically closed field of characteristic 0.Comment: 30 pages (To appear in Commentarii Mathematici Helvetici

Three-Dimensional Solvable Artin Representations Ramified at One Prime

We classify the possibilities for the fixed field of the kernel of an irreducible three-dimensional Artin representation of \Q with solvable image ramified at one prime by using the classification of the finite irreducible subgroups of \PGL_3(\C). This allows us to bound the number of such representations with given Artin conductor

Partial normalizations of coxeter arrangements and discriminants

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