A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions
- 1 December 1985
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 37 (6) , 1149-1162
- https://doi.org/10.4153/cjm-1985-062-4
Abstract
Let R = k[X1, …, 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.Keywords
This publication has 1 reference indexed in Scilit:
- Algebraic GeometryPublished by Springer Nature ,1977