Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Automorphisms mapping a point into a subvariety

Author: Bjorn Poonen; with an appendix by Matthias Aschenbrenner
Journal: J. Algebraic Geom. 20 (2011), 785-794
Published electronically: March 14, 2011
MathSciNet review: 2819676
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Abstract | References | Additional Information

Abstract: 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 $ \mathbb{Z}$ defining an affine $ \mathbb{Q}$-variety whose projective closure is smooth.

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Additional Information

Bjorn Poonen
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307

Matthias Aschenbrenner
Affiliation: Department of Mathematics, University of California Los Angeles, P. O. Box 951555, Los Angeles, California 90095-1555

Received by editor(s): March 27, 2009
Received by editor(s) in revised form: July 14, 2009
Published electronically: March 14, 2011
Additional Notes: The first author was partially supported by NSF grant DMS-0841321. The second author was partially supported by NSF grant DMS-0556197