A Note on Noncancellable Varieties

Abstract

Given two affine algebraic varieties X and Y such that X × ℂ ≅ Y × ℂ, it may happen that X and Y are not isomorphic. This is shown, for example, by so-called “Danielewski surfaces.” In this note, we give a simple construction of such varieties X, Y of an arbitrary dimension n > 1.

Key Words:

• Cancellation problem

2000 Mathematics Subject Classification:

• 14R10