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Cohen–Macaulayness of Rees Algebras of Modules

We provide the sufficient conditions for Rees algebras of modules to be Cohen–Macaulay, which has been proven in the case of Rees algebras of ideals in [11] and [4]. As it turns out the generalization from ideals to modules is not just a routine generalization, but requires a great deal of technical development. We use the technique of generic Bourbaki ideals introduced by Simis, Ulrich, and Vasconcelos [14] to obtain the Cohen–Macaulayness of Rees Algebras of modules.