On set-theoretic complete intersections for smooth curves in three-dimensional affine schemes

2025/11/10 by Lisa Mandal, Mandal, Lisa, Md. Ali Zinna +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2511.07589

Abstract

We prove that every local complete intersection curve in Spec(A), where A is a commutative Noetherian ring of dimension three, is a set-theoretic complete intersection. An analogous result is established for local complete intersection surfaces when A is a four-dimensional affine algebra over the algebraic closure of a finite field of p elements. Furthermore, we show that any local complete intersection curve (respectively, surface) in Spec(A), where A has dimension three (respectively, four), having trivial conormal bundle is, in fact, a complete intersection.

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