Non cancellation for smooth contractible affine threefolds

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.
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Submitted on : Monday, April 26, 2010 - 3:04:58 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Tuesday, September 28, 2010 - 12:48:17 PM

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  • HAL Id : hal-00476471, version 1
  • ARXIV : 1004.4723

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

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