Automorphisms mapping a point into a subvariety
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...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Mathematical Society (AMS)/University Press Inc.
2012
|
| Online Access: | http://hdl.handle.net/1721.1/71609 https://orcid.org/0000-0002-8593-2792 |
| _version_ | 1826216214691577856 |
|---|---|
| author | Poonen, Bjorn Aschenbrenner, Matthias |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Poonen, Bjorn Aschenbrenner, Matthias |
| author_sort | Poonen, Bjorn |
| collection | MIT |
| description | 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 Z defining an affine Q-variety whose projective closure is smooth. |
| first_indexed | 2024-09-23T16:44:07Z |
| format | Article |
| id | mit-1721.1/71609 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:44:07Z |
| publishDate | 2012 |
| publisher | American Mathematical Society (AMS)/University Press Inc. |
| record_format | dspace |
| spelling | mit-1721.1/716092022-10-03T07:53:46Z Automorphisms mapping a point into a subvariety Poonen, Bjorn Aschenbrenner, Matthias Massachusetts Institute of Technology. Department of Mathematics Poonen, Bjorn Poonen, Bjorn 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 Z defining an affine Q-variety whose projective closure is smooth. National Science Foundation (U.S.) (NSF grant DMS-0841321) National Science Foundation (U.S.) (NSF grant DMS-0556197) 2012-07-12T20:09:45Z 2012-07-12T20:09:45Z 2011-03 2009-07 Article http://purl.org/eprint/type/JournalArticle 1056-3911 1534-7486 http://hdl.handle.net/1721.1/71609 Poonen, Bjorn. “Automorphisms Mapping a Point into a Subvariety.” Journal of Algebraic Geometry 20.4 (2011): 785–794. Web. https://orcid.org/0000-0002-8593-2792 en_US http://dx.doi.org/10.1090/S1056-3911-2011-00543-2 Journal of Algebraic Geometry Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf American Mathematical Society (AMS)/University Press Inc. MIT web domain |
| spellingShingle | Poonen, Bjorn Aschenbrenner, Matthias Automorphisms mapping a point into a subvariety |
| title | Automorphisms mapping a point into a subvariety |
| title_full | Automorphisms mapping a point into a subvariety |
| title_fullStr | Automorphisms mapping a point into a subvariety |
| title_full_unstemmed | Automorphisms mapping a point into a subvariety |
| title_short | Automorphisms mapping a point into a subvariety |
| title_sort | automorphisms mapping a point into a subvariety |
| url | http://hdl.handle.net/1721.1/71609 https://orcid.org/0000-0002-8593-2792 |
| work_keys_str_mv | AT poonenbjorn automorphismsmappingapointintoasubvariety AT aschenbrennermatthias automorphismsmappingapointintoasubvariety |