English

Automorphisms mapping a point into a subvariety

Algebraic Geometry 2017-04-03 v1 Number Theory

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.

Keywords

Cite

@article{arxiv.0902.3571,
  title  = {Automorphisms mapping a point into a subvariety},
  author = {Bjorn Poonen},
  journal= {arXiv preprint arXiv:0902.3571},
  year   = {2017}
}

Comments

5 pages

R2 v1 2026-06-21T12:13:47.542Z