Automorphisms mapping a point into a subvariety
Author(s)Poonen, Bjorn; Aschenbrenner, Matthias
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Algebraic Geometry
American Mathematical Society (AMS)/University Press Inc.
Poonen, Bjorn. “Automorphisms Mapping a Point into a Subvariety.” Journal of Algebraic Geometry 20.4 (2011): 785–794. Web.
Author's final manuscript