Automorphisms mapping a point into a subvariety

Automorphisms mapping a point into a subvariety

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...

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Bibliographic Details
Main Authors: Poonen, Bjorn (Contributor), Aschenbrenner, Matthias (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: American Mathematical Society (AMS)/University Press Inc., 2012-07-12T20:09:45Z.
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Summary: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.
National Science Foundation (U.S.) (NSF grant DMS-0841321)
National Science Foundation (U.S.) (NSF grant DMS-0556197)

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