On the equations defining curves in a polynomial algebra

2005/08/17 by Ze Min Zeng, Zeng, Ze Min
Computer Science · Mathematics · #13C10 #13C40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13C10 #msc:13C40

paper · pdf · doi:10.48550/arxiv.math/0508304

11 pages. Accepted by the journal Communications in Algebra

arxiv created 2005/08/17 · openalex publication_date 2005/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a commutative Noetherian ring of dimension n (n ≥ 3). Let I be a local complete intersection ideal in A[T] of height n. Suppose I/I² is free A[T]/I-module of rank n and (A[T]/I) is torsion in K₀(A[T]). It is proved in this paper that I is a set theoretic complete intersection ideal in A[T] if one of the following conditions holds: (1) n ≥ 5, odd; (2) n is even, and A contains the field of rational numbers; (3) n = 3, and A contains the field of rational numbers.

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