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We construct the minimal resolutions of three classes of monomial ideals:dominant, 1-semidominant, and 2-semidominant ideals. The families of dominantand 1-semidominant ideals extend those of complete and almost completeintersections. We show that dominant ideals give a precise characterization ofwhen the Taylor resolution is minimal, 1-semidominant ideals are Scarf, and theminimal resolutions of 2-semidominant ideals can be obtained from their Taylorresolutions by eliminating faces and facets of equal multidegree, in arbitraryorder. We study the combinatorial properties of these classes of ideals andexplain how they relate to generic ideals.

Minimal Resolutions of Dominant and Semidominant Ideals