Non cancellation for smooth contractible affine threefolds

Adrien Dubouloz (1) , Lucy Moser-Jauslin (1) , Pierre-Marie Poloni (1, 2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Unibas - Université de Bâle = University of Basel = Basel Universität

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.

Mots clés: Cancellation Problem; contractible affine threefolds; exotic affine spaces

Domaines: Géométrie algébrique [math.AG]

Adrien Dubouloz, Lucy Moser-Jauslin, Pierre-Marie Poloni. Non cancellation for smooth contractible affine threefolds. 2010. ⟨hal-00476471⟩