October 16, 2025Open Access

Rees algebra and almost linearly presented ideals in three variables

Key Points

Explicit formulas for the defining ideal of the Rees algebra are obtained from height two perfect ideals.
The ideal considered has rank one after taking a quotient by an ideal generated by two variables.
Almost linearly presented ideals show linear entries except for a last column with degree two entries.
The ideal satisfies conditions for $ ext{Gs}2$ but not $ ext{Gs}3$, impacting the Rees algebra's structure.

Abstract

Let R=, y, z and I= (f₀, , f₍-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 2 but not 3, then we obtain explicit formulas for the defining ideal of the Rees algebra (I) of I.

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Cite This Study

Suraj Kumar (Thu,) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e9b7 https://doi.org/https://doi.org/10.48550/arxiv.2506.21491

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