RATIONALITY OF FIELDS OF INVARIANTS OF SOME FOUR-DIMENSIONAL LINEAR GROUPS, AND AN EQUIVARIANT CONSTRUCTION RELATED TO THE SEGRE CUBIC

Abstract

Let be a finite primitive linear group. We prove that if contains a normal subgroup of order 32 then the quotient variety is birationally isomorphic to , where is the Segre cubic. We also prove the rationality of for a large class of such groups (in particular, solvable groups).