Modules of Constant Jordan Type with Small Non-Projective Part

Abstract

Let E be an elementary abelian p-group of rank r and let k be an algebraically closed field of characteristic p. We prove that if M is a kE-module of stable constant Jordan type [a 1]...[a t ] with ∑ j a j ≤ min(r − 1, p − 2) then a 1 = ... = a t = 1. The proof uses the theory of Chern classes of vector bundles on projective space.