On Rees algebras of 2-determinantal ideals

On Rees algebras of 2-determinantal ideals

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...

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Veröffentlicht in:arXiv.org 2023-11
Hauptverfasser: Ramkumar, Ritvik, Sammartano, Alessio
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Algebra
Mathematical analysis
Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
Stratification
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description 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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subjects Algebra
Mathematical analysis
Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
Stratification
title On Rees algebras of 2-determinantal ideals
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