Geodesic
A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1149-1162

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Let R = k[X 1, ..., Xn ] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the form Some of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di . 
Huneke, Craig; Miller, Matthew. A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1149-1162. doi: 10.4153/CJM-1985-062-4
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