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Article: Affine varieties with equivalent cylinders

TitleAffine varieties with equivalent cylinders
Authors
Issue Date2002
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2002, v. 251 n. 1, p. 295-307 How to Cite?
AbstractA well-known cancellation problem asks when, for two algebraic varieties V1, V2 ⊆ Cn, the isomorphism of the cylinders V1 × C and V2 × C implies the isomorphism of V1 and V2. In this paper, we address a related problem: when the equivalence (under an automorphism of Cn+1) of two cylinders V1 × C and V2 × C implies the equivalence of their bases V1 and V2 under an automorphism of Cn. We concentrate here on hypersurfaces and show that this problem establishes a strong connection between the cancellation conjecture of Zariski and the embedding conjecture of Abhyankar and Sathaye. We settle the problem in the affirmative for a large class of polynomials. On the other hand, we give examples of equivalent cylinders with inequivalent bases. (Those cylinders, however, are not hypersurfaces.) Another result of interest is that, for an arbitrary field K, the equivalence of two polynomials in m variables under an automorphism of K[x1,⋯,xn], n ≥ m, implies their equivalence under a tame automorphism of K[x1,⋯,x2n]. © 2002 Elsevier Science (USA).
Persistent Identifierhttp://hdl.handle.net/10722/75127
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorShpilrain, Ven_HK
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:08:10Z-
dc.date.available2010-09-06T07:08:10Z-
dc.date.issued2002en_HK
dc.identifier.citationJournal Of Algebra, 2002, v. 251 n. 1, p. 295-307en_HK
dc.identifier.issn0021-8693en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75127-
dc.description.abstractA well-known cancellation problem asks when, for two algebraic varieties V1, V2 ⊆ Cn, the isomorphism of the cylinders V1 × C and V2 × C implies the isomorphism of V1 and V2. In this paper, we address a related problem: when the equivalence (under an automorphism of Cn+1) of two cylinders V1 × C and V2 × C implies the equivalence of their bases V1 and V2 under an automorphism of Cn. We concentrate here on hypersurfaces and show that this problem establishes a strong connection between the cancellation conjecture of Zariski and the embedding conjecture of Abhyankar and Sathaye. We settle the problem in the affirmative for a large class of polynomials. On the other hand, we give examples of equivalent cylinders with inequivalent bases. (Those cylinders, however, are not hypersurfaces.) Another result of interest is that, for an arbitrary field K, the equivalence of two polynomials in m variables under an automorphism of K[x1,⋯,xn], n ≥ m, implies their equivalence under a tame automorphism of K[x1,⋯,x2n]. © 2002 Elsevier Science (USA).en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_HK
dc.relation.ispartofJournal of Algebraen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleAffine varieties with equivalent cylindersen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-8693&volume=251 no1&spage=295&epage=307&date=2002&atitle=Affine+varieties+with+equivalent+cylindersen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1006/jabr.2001.9124en_HK
dc.identifier.scopuseid_2-s2.0-0036575745en_HK
dc.identifier.hkuros75659en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0036575745&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume251en_HK
dc.identifier.issue1en_HK
dc.identifier.spage295en_HK
dc.identifier.epage307en_HK
dc.identifier.isiWOS:000176070700015-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridShpilrain, V=6603904879en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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