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FALL 2014 Koszul property of diagonal subalgebras
Neeraj Kumar
J. Commut. Algebra 6(3): 385-406 (FALL 2014). DOI: 10.1216/JCA-2014-6-3-385

Abstract

Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and $I$ a homogeneous ideal in $S$ generated by a regular sequence $f_1,f_2, \ldots,f_k$ of homogeneous forms of degree~$d$. We study a generalization of a result of Conca et al.~\cite{CHTV} concerning Koszul property of the diagonal subalgebras associated to $I$. Each such subalgebra has the form $K[(I^e)_{ed+c}]$, where $c,e \in \mathbf{N}$. For $k=3$, we extend \cite[Corollary 6.10]{CHTV} by proving that $K[(I^e)_{ed+c}]$ is Koszul as soon as $c \geq {d}/{2}$ and $e >0$. We also extend \cite[Corollary 6.10]{CHTV} in another direction by replacing the polynomial ring with a Koszul ring.

Citation

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Neeraj Kumar. "Koszul property of diagonal subalgebras." J. Commut. Algebra 6 (3) 385 - 406, FALL 2014. https://doi.org/10.1216/JCA-2014-6-3-385

Information

Published: FALL 2014
First available in Project Euclid: 17 November 2014

zbMATH: 1304.13026
MathSciNet: MR3278810
Digital Object Identifier: 10.1216/JCA-2014-6-3-385

Subjects:
Primary: 13D02
Secondary: 13S37

Keywords: complete intersection , diagonal subalgebra , Koszul algebra , Rees algebra

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.6 • No. 3 • FALL 2014
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