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Article: The stable equivalence and cancellation problems

TitleThe stable equivalence and cancellation problems
Authors
KeywordsAlgebraic varieties
Cancellation problem
Danielewski surfaces
Polynomial automorphisms
Stable equivalence
Issue Date2004
PublisherSchweizerische 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?
AbstractLet 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 Identifierhttp://hdl.handle.net/10722/75260
ISSN
2015 Impact Factor: 1.045
2015 SCImago Journal Rankings: 2.553
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorMakarLimanov, Len_HK
dc.contributor.authorVan Rossum, Pen_HK
dc.contributor.authorShpilrain, Ven_HK
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:09:27Z-
dc.date.available2010-09-06T07:09:27Z-
dc.date.issued2004en_HK
dc.identifier.citationCommentarii Mathematici Helvetici, 2004, v. 79 n. 2, p. 341-349en_HK
dc.identifier.issn0010-2571en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75260-
dc.description.abstractLet 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.languageengen_HK
dc.publisherSchweizerische Mathematische Gesellschaft. The Journal's web site is located at http://link.springer.de/link/service/journals/00014/index.htmen_HK
dc.relation.ispartofCommentarii Mathematici Helveticien_HK
dc.subjectAlgebraic varietiesen_HK
dc.subjectCancellation problemen_HK
dc.subjectDanielewski surfacesen_HK
dc.subjectPolynomial automorphismsen_HK
dc.subjectStable equivalenceen_HK
dc.titleThe stable equivalence and cancellation problemsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://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+problemsen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s00014-003-0796-3en_HK
dc.identifier.scopuseid_2-s2.0-2442621623en_HK
dc.identifier.hkuros89504en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-2442621623&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume79en_HK
dc.identifier.issue2en_HK
dc.identifier.spage341en_HK
dc.identifier.epage349en_HK
dc.identifier.isiWOS:000221445800006-
dc.publisher.placeSwitzerlanden_HK
dc.identifier.scopusauthoridMakarLimanov, L=6603475677en_HK
dc.identifier.scopusauthoridVan Rossum, P=36768668300en_HK
dc.identifier.scopusauthoridShpilrain, V=6603904879en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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