Noncancellation for contractible affine threefolds

Dubouloz, Adrien; Moser-Jauslin, Lucy; Poloni, P.-M.

doi:10.1090/S0002-9939-2011-10869-4

Noncancellation for contractible affine threefolds
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by Adrien Dubouloz, Lucy Moser-Jauslin and P.-M. Poloni

Proc. Amer. Math. Soc. 139 (2011), 4273-4284

DOI: https://doi.org/10.1090/S0002-9939-2011-10869-4

Published electronically: May 2, 2011

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Abstract:

We construct two nonisomorphic contractible affine threefolds $X$ and $Y$ with the property that their cylinders $X\times \mathbb {A}^{1}$ and $Y\times \mathbb {A}^{1}$ are isomorphic, 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 $\mathbb {A}^{3}$’s.

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