Minimal free resolutions of general points lying on cubic surfaces in P3

Casanellas has shown that a generalized version of Lorenzini’s Minimal Resolution Conjecture (as modified by Mustaţaˇ) holds for a set of t general points on a smooth cubic surface in P3, for certain specific values of t. We extend her work by verifying the conjecture for all t, and by allowing the cubic surface to have isolated double points.