Defining equations of the Rees algebra of certain parametric surfaces

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Let f0, f1, f2, f3 be linearly independent nonzero homogeneous polynomials in the standard ℤ-graded ring R := K[s, t, u] of the same degree d, and gcd(f0, f1, f2, f3) = 1. This defines a rational map ℙ2 → ℙ3. The Rees algebra Rees(I) = R ⊕ I ⊕ I2 ⊕ ⋯ of the ideal I = 〈f 0, f1, f2, f3〉 is the graded R-algebra which can be described as the image of the R-algebra homomorphism h: R[x, y, z, w ] → Rees(I). This paper discusses one result concerning the structure of the kernel of the map h when I is a saturated local complete intersection ideal with V(I) ≠ ∅ and μ-basis of degrees (1,1,d - 2). © 2010 World Scientific Publishing Company.

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Journal of Algebra and its Applications

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