PLANES OF MATRICES OF CONSTANT RANK AND GLOBALLY GENERATED VECTOR BUNDLES

We consider the problem of determining all pairs (c(1), c(2)) of Chern classes of rank 2 bundles that are cokernel of a skew-symmetric matrix of linear forms in 3 variables, having constant rank 2c(1) and size 2c(1) +2. We completely solve the problem in the "stable" range, i.e. for pairs with c(1)(2)-4c(2) < 0, proving that the additional condition c(2) <= ((c1+1)(2)) is necessary and sufficient. For c(1)(2)-4c(2) >= 0, we prove that there exist globally generated bundles, some even defining an embedding of P-2 in a Grassmannian, that cannot correspond to a matrix of the above type. This extends previous work on c(1) <= 3.