  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.

Algebraic Geometry;Number Theory