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arXiv · 2506.21491

Rees algebra and almost linearly presented ideals in three variables

Suraj Kumar
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Abstract

Let $R=\k[x,y,z]$ and $I=(f_0,\dots,f_{n-1})$ be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$). Further we suppose that after modulo an ideal generated by two variables, the presentation matrix has rank one. Also, the ideal $I$ satisfies $\Gs{{2}}$ but not $\Gs{3}$, then we obtain explicit formulas for the defining ideal of the Rees algebra $\rees(I)$ of $I$.

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Suraj Kumar. 2025-06-26. Rees algebra and almost linearly presented ideals in three variables. https://arxiv.org/abs/2506.21491

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