Residual intersections and modules with Cohen-Macaulay Rees algebra

Costantini, Alessandra

doi:10.48550/arxiv.1811.08402

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2020

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“…In particular, with some additional assumptions on the module E, we can give more explicit sufficient conditions for F pEq to be Cohen-Macaulay. The next two corollaries exploit results on the Cohen-Macaulay property of Rees rings from [7] and recover [4, 2.9] in the case when E is an ideal of grade at least two.…”

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confidence: 78%

Cohen-Macaulay fiber cones and defining ideal of Rees algebras of modules

Costantini¹

2020

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Generic Bourbaki ideals were introduced by Simis, Ulrich and Vasconcelos in [41] to study the Cohen-Macaulay property of Rees algebras of modules. In this article we prove that the same technique can sometimes be used to investigate the Cohen-Macaulay property of fiber cones of modules and to study the defining ideal of Rees algebras. This is possible as long as the Rees algebra of a given module E is a deformation of the Rees algebra of a generic Bourbaki ideal I of E. Our main technical result provides a deformation condition that in fact extends the applicability of generic Bourbaki ideals to situations not covered in [41].[51] M. Weaver, Rees algebras of ideals and modules over hypersurface and complete intersection rings, Ph.D. thesis, Purdue University, in preparation.

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confidence: 78%