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arXiv · 2101.03222

Rees algebras of sparse determinantal ideals

Ela Celikbas·Emilie Dufresne·Louiza Fouli·Elisa Gorla·Kuei-Nuan Lin·Claudia Polini·Irena Swanson
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Abstract

We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a $2\times n$ sparse matrix. We prove that their initial algebras are ladder determinantal rings. This allows us to show that the Rees algebra and the special fiber ring are Cohen-Macaulay domains, they are Koszul, they have rational singularities in characteristic zero and are F-rational in positive characteristic.

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Ela Celikbas, Emilie Dufresne, Louiza Fouli, Elisa Gorla, Kuei-Nuan Lin, Claudia Polini, Irena Swanson. 2021-01-08. Rees algebras of sparse determinantal ideals. https://arxiv.org/abs/2101.03222

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