Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Noncancellation for contractible affine threefolds


Authors: Adrien Dubouloz, Lucy Moser-Jauslin and P.-M. Poloni
Journal: Proc. Amer. Math. Soc. 139 (2011), 4273-4284
MSC (2010): Primary 14R10
Published electronically: May 2, 2011
MathSciNet review: 2823073
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14R10

Retrieve articles in all journals with MSC (2010): 14R10


Additional Information

Adrien Dubouloz
Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary - BP 47870, 21078 Dijon cedex, France
Email: Adrien.Dubouloz@u-bourgogne.fr

Lucy Moser-Jauslin
Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary - BP 47870, 21078 Dijon cedex, France
Email: moser@u-bourgogne.fr

P.-M. Poloni
Affiliation: Mathematisches Institut, Universitat Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
Email: pierre-marie.poloni@unibas.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10869-4
PII: S 0002-9939(2011)10869-4
Received by editor(s): June 30, 2010
Received by editor(s) in revised form: October 23, 2010
Published electronically: May 2, 2011
Communicated by: Lev Borisov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.