Rees algebra and almost linearly presented ideals in three variables

2025/06/26 by Suraj Kumar, Kumar, Suraj
Mathematics · #13A30 #13C14 #13H10 #13H15 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2506.21491

openalex publication_date 2025/06/26 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

Let R=\k[x,y,z] and I=(f₀,…,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 \Gs2 but not \Gs3, then we obtain explicit formulas for the defining ideal of the Rees algebra \rees(I) of I.

Citations

• On Rees algebras of linearly presented ideals and modules
• On Rees algebras of ideals and modules over hypersurface rings
• Equations defining certain graphs
• Linearly presented perfect ideals of codimension 2 in three variables
• Minimal generators of the defining ideal of the Rees Algebra associated to a rational plane parameterization with μ=2
• Rational Normal Scrolls and the Defining Equations of Rees Algebras
• On the equations of the moving curve ideal of a rational algebraic plane curve
• On the homology of two-dimensional elimination

Related

• On Rees algebras of linearly presented ideals and modules
• The equations of Rees algebras of ideals of almost-linear type
• Linearly presented perfect ideals of codimension 2 in three variables
• Equations of Rees algebras of ideals in two variables
• On the defining equations of Rees algebra of a height two perfect ideal using the theory of D-modules