An Analytic Approach to The Cancellation Problem for Affine Spaces over ℂ

2006/11/13 by Oda, Susumu
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0611367

Abstract

The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that : Let k be an algebraically closed field of characteristic zero and let n, m ∈ ℕ. If R[Y₁,..., Y_m] ≅_k k[X₁,..., X_n+m] as k-algebras, where Y₁,..., Y_m, X₁,..., X_n+m are indeterminates, then R ≅_k k[X₁,..., X_n].

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