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Article: The stable equivalence and cancellation problems
Title | The stable equivalence and cancellation problems |
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Authors | |
Keywords | Algebraic varieties Cancellation problem Danielewski surfaces Polynomial automorphisms Stable equivalence |
Issue Date | 2004 |
Publisher | Schweizerische Mathematische Gesellschaft. The Journal's web site is located at http://link.springer.de/link/service/journals/00014/index.htm |
Citation | Commentarii Mathematici Helvetici, 2004, v. 79 n. 2, p. 341-349 How to Cite? |
Abstract | Let K be an arbitrary field of characteristic 0, and An the n-dimensional affine space over K. A well-known cancellation problem asks, given two algebraic varieties V1, V2 ⊆ An with isomorphic cylinders V1 × A1 and V2 × A1, whether V1 and V2 themselves are isomorphic. In this paper, we focus on a related problem: given two varieties with equivalent (under an automorphism of An+1) cylinders V 1 × A1 and V2 × A1, are V1 and V2 equivalent under an automorphism of A n ? We call this stable equivalence problem. We show that the answer is positive for any two curves V1, V2 ⊆ A 2. For an arbitrary n ≥ 2, we consider a special, arguably the most important, case of both problems, where one of the varieties is a hyperplane. We show that a positive solution of the stable equivalence problem in this case implies a positive solution of the cancellation problem. |
Persistent Identifier | http://hdl.handle.net/10722/75260 |
ISSN | 2023 Impact Factor: 1.1 2023 SCImago Journal Rankings: 1.434 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | MakarLimanov, L | en_HK |
dc.contributor.author | Van Rossum, P | en_HK |
dc.contributor.author | Shpilrain, V | en_HK |
dc.contributor.author | Yu, JT | en_HK |
dc.date.accessioned | 2010-09-06T07:09:27Z | - |
dc.date.available | 2010-09-06T07:09:27Z | - |
dc.date.issued | 2004 | en_HK |
dc.identifier.citation | Commentarii Mathematici Helvetici, 2004, v. 79 n. 2, p. 341-349 | en_HK |
dc.identifier.issn | 0010-2571 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75260 | - |
dc.description.abstract | Let K be an arbitrary field of characteristic 0, and An the n-dimensional affine space over K. A well-known cancellation problem asks, given two algebraic varieties V1, V2 ⊆ An with isomorphic cylinders V1 × A1 and V2 × A1, whether V1 and V2 themselves are isomorphic. In this paper, we focus on a related problem: given two varieties with equivalent (under an automorphism of An+1) cylinders V 1 × A1 and V2 × A1, are V1 and V2 equivalent under an automorphism of A n ? We call this stable equivalence problem. We show that the answer is positive for any two curves V1, V2 ⊆ A 2. For an arbitrary n ≥ 2, we consider a special, arguably the most important, case of both problems, where one of the varieties is a hyperplane. We show that a positive solution of the stable equivalence problem in this case implies a positive solution of the cancellation problem. | en_HK |
dc.language | eng | en_HK |
dc.publisher | Schweizerische Mathematische Gesellschaft. The Journal's web site is located at http://link.springer.de/link/service/journals/00014/index.htm | en_HK |
dc.relation.ispartof | Commentarii Mathematici Helvetici | en_HK |
dc.subject | Algebraic varieties | en_HK |
dc.subject | Cancellation problem | en_HK |
dc.subject | Danielewski surfaces | en_HK |
dc.subject | Polynomial automorphisms | en_HK |
dc.subject | Stable equivalence | en_HK |
dc.title | The stable equivalence and cancellation problems | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0010-2571&volume=79 no2&spage=341&epage=349&date=2004&atitle=The+stable+equivalence+and+cancellation+problems | en_HK |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_HK |
dc.identifier.authority | Yu, JT=rp00834 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00014-003-0796-3 | en_HK |
dc.identifier.scopus | eid_2-s2.0-2442621623 | en_HK |
dc.identifier.hkuros | 89504 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-2442621623&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 79 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 341 | en_HK |
dc.identifier.epage | 349 | en_HK |
dc.identifier.isi | WOS:000221445800006 | - |
dc.publisher.place | Switzerland | en_HK |
dc.identifier.scopusauthorid | MakarLimanov, L=6603475677 | en_HK |
dc.identifier.scopusauthorid | Van Rossum, P=36768668300 | en_HK |
dc.identifier.scopusauthorid | Shpilrain, V=6603904879 | en_HK |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_HK |
dc.identifier.issnl | 0010-2571 | - |