Bundles on Pn with vanishing lower cohomologies

We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathbf{M}$ according to the Hilbert function $H$ and classify all possible Hilbert functions $H$ of such bundles. For each $H$, we describe a stratification of ${\mathbf{M}}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice given by the Betti numbers.