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Homological Criteria for Minimal Multiplicity
If a commutative noetherian local ring R happens to fall into one of several subclasses of such rings, then lower bounds on its Hilbert-Samuel multiplicity are known in terms of other numerical invariants; rings which achieve these lower bounds are said to have minimal multiplicity and have several desirable properties. This dissertation provides several homological criteria for a ring to have minimal multiplicity, some criteria based on the structure of Ext-algebras and others on a numerical homological invariant called linearity defect.
Myers, John, "Homological Criteria for Minimal Multiplicity" (2017). ETD collection for University of Nebraska - Lincoln. AAI10272322.