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.
Categories: math.AG math.AC