Modules of constant Jordan type with two non-projective blocks

Let E be an elementary abelian p-group of rank r and let k be an algebraically closed field of characteristic p. We investigate finitely generated kE-modules M of stable constant Jordan type [a][b] for 1⩽a,b⩽p−1 using the functors Fi from modules of constant Jordan type to vector bundles on projective space Pr−1 constructed by Benson and Pevtsova (in press) [3].In particular, we study relations on the first few Chern numbers of the trivial bundle to obtain restrictions on the values of a and b for sufficiently large ranks and primes. Finally, we use similar techniques to find restrictions on the values of p and r for which there exist modules of stable constant Jordan type [3][2][1].