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arXiv · 2601.18153

On Golod Subdeterminantal Ideals

Omkar Javadekar
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Abstract

Let $X=(x_{ij})_{m\times n}$ be a matrix of indeterminates and let $S=\mathbb{k}[x_{ij} \mid 1\leq i\leq m,\ 1\leq j\leq n]$ be a polynomial ring over an infinite field $\mathbb{k}$. Let $I$ be an ideal generated by a subset of the set of all $2\times2$ minors of $X$. We show that the quotient ring $S/I$ is Golod if and only if $I=I_2(Y)$ for some $2\times \ell$ or $\ell\times2$ submatrix $Y$ of $X$. In fact, we prove that Golodness of $S/I$ is equivalent to the triviality of the product on the Koszul homology of $S/I$ and to $I$ having a linear resolution. Along the way, we also prove a result on the non-Golodness of tensor products of rings under certain conditions.

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Omkar Javadekar. 2026-01-26. On Golod Subdeterminantal Ideals. https://arxiv.org/abs/2601.18153

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