Automorphisms mapping a point into a subvariety

Automorphisms mapping a point into a subvariety

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Bjorn Poonen, MIT
Fine Hall 322

Given a variety $X$, a point $x$ in $X$, and a subvariety $Z$ of $X$, is there an automorphism of $X$ mapping $x$ into $Z$?  We prove that this problem is undecidable.