Fibers of Generic Brauer–Severi Schemes

In this note we investigate the fibers of Van den Berghʹs Brauer–Severi scheme of the trace ring ofmgenericn × nmatrices over the variety of matrix-invariants. If ξ Vm, nis a point of representation type (m1, n1;…; mr, nr), then the reduced variety of η − 1(ξ) has (∑mi)!/∏mi! irreducible components each of dimension [equation]