\title{Modules of constant Jordan type with small non-projective part}
\author{David J. Benson}
\address{Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE}
\begin{document}
\begin{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 $[a_1]\dots[a_t]$ with
$\sum_ja_j\le\min(r-1,p-2)$ then $a_1=\dots=a_t=1$. The proof uses the
theory of Chern classes of vector bundles on projective space.
\end{abstract}