Automorphisms mapping a point into a subvariety

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.

5 pages

References in corpus (1)

• Hilbert's Tenth Problem for function fields of varieties over C

Cited by in corpus (2)

• The isomorphism problem of projective schemes and related algorithmic problems
• On modular computation of Groebner bases with integer coefficients