  Given a zero-dimensional scheme Z, the higher-rank interpolation problem asks
for the classification of slopes of vector bundles cohomologically orthogonal
to the ideal sheaf of Z. In this paper, we solve this problem for all
zero-dimensional monomial schemes in the projective plane. As a corollary, we
obtain detailed information on the stable base loci of divisors on the Hilbert
scheme of points on the plane. We prove the correspondence between walls in the
Bridgeland stability manifold and walls in the Mori chamber decomposition of
the effective cone conjectured by Arcara-Bertram-Coskun-Huizenga for monomial
schemes. We determine the Harder-Narasimhan filtration of ideal sheaves of
monomial schemes for suitable Bridgeland stability conditions and, as a
consequence, obtain a new resolution better suited for cohomology computations
than other standard resolutions such as the minimal free resolution.
