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arXiv · 0902.3571

Automorphisms mapping a point into a subvariety

Bjorn Poonen
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Abstract

The problem of deciding, given a complex variety X, a point x in X, and a subvariety Z of 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.

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Bjorn Poonen. 2009-02-20. Automorphisms mapping a point into a subvariety. https://doi.org/10.1090/s1056-3911-2011-00543-2

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