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arXiv · 2210.12668

On Rees algebras of 2-determinantal ideals

Ritvik Ramkumar·Alessio Sammartano
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Abstract

Let I be the ideal of minors of a 2 by n matrix of linear forms with the expected codimension. In this paper we prove that the Rees algebra of I and its special fiber ring are Cohen-Macaulay and Koszul; in particular, they are quadratic algebras. The main novelty in our approach is the analysis of a stratification of the Hilbert scheme of determinantal ideals. We study degenerations of Rees algebras along this stratification, and combine it with certain squarefree Groebner degenerations.

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Ritvik Ramkumar, Alessio Sammartano. 2022-10-23. On Rees algebras of 2-determinantal ideals. https://doi.org/10.1112/jlms.12821

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