Non cancellation for smooth contractible affine threefolds

2010/04/27 by Dubouloz, Adrien, Moser-Jauslin, Lucy, Poloni, Pierre-Marie
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1004.4723

Abstract

We construct two non isomorphic contractible affine threefolds X and Y with isomorphic cylinders, showing that the generalized Cancellation Problem has a negative answer in general for contractible affine threefolds. We also establish that X and Y are actually biholomorphic as complex analytic varieties, providing the first example of a pair of biholomorphic but not isomorphic exotic affine 3-spaces.

Related

• Factorial threefolds with Ga-actions
• Algebraic families of higher dimensional \mathbbA¹-contractible affine varieties non-isomorphic to affine spaces
• Affine open subsets in A³ without the cancellation property
• The Automorphism Group of Certain Factorial Threefolds and a Cancellation Problem
• A Counter-example to the Cancellation Problem for the Affine Space A³ in characteristic p