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Automorphisms mapping a point into a subvariety

Author(s)
Poonen, Bjorn; Aschenbrenner, Matthias
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Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/
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Abstract
The problem of deciding, given a complex variety X, a point x \in X, and a subvariety Z \subseteq X, whether there is an automorphism of X mapping x into Z is proved undecidable. Along the way, we prove the undecidability of a version of Hilbert's tenth problem for systems of polynomials over Z defining an affine Q-variety whose projective closure is smooth.
Date issued
2011-03
URI
http://hdl.handle.net/1721.1/71609
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Algebraic Geometry
Publisher
American Mathematical Society (AMS)/University Press Inc.
Citation
Poonen, Bjorn. “Automorphisms Mapping a Point into a Subvariety.” Journal of Algebraic Geometry 20.4 (2011): 785–794. Web.
Version: Author's final manuscript
ISSN
1056-3911
1534-7486

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