In this paper we prove that a generalized version of the Minimal Resolution Conjecture given by Musta\c{t}\v{a} holds for certain general sets of points on a smooth cubic surface $X \subset \PP^3$. The main tool used is Gorenstein liaison theory and, more precisely, the relationship between the free resolutions of two linked schemes.

MSC Classifications:

13D02, 13C40, 14M05, 14M07 show english descriptions Syzygies, resolutions, complexes
Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]
Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]
Low codimension problems 13D02 - Syzygies, resolutions, complexes
13C40 - Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]
14M05 - Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]
14M07 - Low codimension problems

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