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Article: Birational morphisms of the plane
Title | Birational morphisms of the plane |
---|---|
Authors | |
Keywords | Affine Plane Birational Morphisms Peak Reduction |
Issue Date | 2004 |
Publisher | American Mathematical Society. The Journal's web site is located at http://www.ams.org/proc |
Citation | Proceedings Of The American Mathematical Society, 2004, v. 132 n. 9, p. 2511-2515 How to Cite? |
Abstract | Let A 2 be the affine plane over a field K of characteristic 0. Birational morphisms of A 2 are mappings A 2 → A 2 given by polynomial mappings φ of the polynomial algebra K[x, y] such that for the quotient fields, one has K(φ(x), φ(y)) = K(x, y). Polynomial automorphisms are obvious examples of such mappings. Another obvious example is the mapping τ x given by x → x, y → xy. For a while, it was an open question whether every birational morphism is a product of polynomial automorphisms and copies of τ x. This question was answered in the negative by P. Russell (in an informal communication). In this paper, we give a simple combinatorial solution of the same problem. More importantly, our method yields an algorithm for deciding whether a given birational morphism can be factored that way. |
Persistent Identifier | http://hdl.handle.net/10722/156212 |
ISSN | 2015 Impact Factor: 0.7 2015 SCImago Journal Rankings: 1.082 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Shpilrain, V | en_US |
dc.contributor.author | Yu, JT | en_US |
dc.date.accessioned | 2012-08-08T08:40:51Z | - |
dc.date.available | 2012-08-08T08:40:51Z | - |
dc.date.issued | 2004 | en_US |
dc.identifier.citation | Proceedings Of The American Mathematical Society, 2004, v. 132 n. 9, p. 2511-2515 | en_US |
dc.identifier.issn | 0002-9939 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156212 | - |
dc.description.abstract | Let A 2 be the affine plane over a field K of characteristic 0. Birational morphisms of A 2 are mappings A 2 → A 2 given by polynomial mappings φ of the polynomial algebra K[x, y] such that for the quotient fields, one has K(φ(x), φ(y)) = K(x, y). Polynomial automorphisms are obvious examples of such mappings. Another obvious example is the mapping τ x given by x → x, y → xy. For a while, it was an open question whether every birational morphism is a product of polynomial automorphisms and copies of τ x. This question was answered in the negative by P. Russell (in an informal communication). In this paper, we give a simple combinatorial solution of the same problem. More importantly, our method yields an algorithm for deciding whether a given birational morphism can be factored that way. | en_US |
dc.language | eng | en_US |
dc.publisher | American Mathematical Society. The Journal's web site is located at http://www.ams.org/proc | en_US |
dc.relation.ispartof | Proceedings of the American Mathematical Society | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.rights | First published in [Proceedings of the American Mathematical Society] in [2004, v. 132 n. 9], published by the American Mathematical Society | - |
dc.subject | Affine Plane | en_US |
dc.subject | Birational Morphisms | en_US |
dc.subject | Peak Reduction | en_US |
dc.title | Birational morphisms of the plane | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_US |
dc.identifier.authority | Yu, JT=rp00834 | en_US |
dc.description.nature | published_or_final_version | en_US |
dc.identifier.doi | 10.1090/S0002-9939-04-07490-8 | en_US |
dc.identifier.scopus | eid_2-s2.0-4344713057 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-4344713057&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 132 | en_US |
dc.identifier.issue | 9 | en_US |
dc.identifier.spage | 2511 | en_US |
dc.identifier.epage | 2515 | en_US |
dc.identifier.isi | WOS:000222122200003 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Shpilrain, V=6603904879 | en_US |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |