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arXiv · 2011.08453

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

Alessandra Costantini
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Abstract

Generic Bourbaki ideals were introduced by Simis, Ulrich and Vasconcelos 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 by previous work.

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Alessandra Costantini. 2020-11-15. Cohen-Macaulay fiber cones and defining ideal of Rees algebras of modules. https://arxiv.org/abs/2011.08453

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