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Article: Embeddings of hypersurfaces in affine spaces

TitleEmbeddings of hypersurfaces in affine spaces
Authors
Issue Date2001
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2001, v. 239 n. 1, p. 161-173 How to Cite?
AbstractIn this paper, we address the following two general problems: given two algebraic varieties in Cn, find out whether or not they are (1) isomorphic and (2) equivalent under an automorphism of Cn. Although a complete solution of either of those problems is out of the question at this time, we give here some handy and useful invariants of isomorphic as well as of equivalent varieties. Furthermore, and more importantly, we give a universal procedure for obtaining all possible algebraic varieties isomorphic to a given one and use it to construct numerous examples of isomorphic but inequivalent algebraic varieties in Cn. Among other things, we establish the following interesting fact: for isomorphic hypersurfaces p(x1,...,xn)=0 and q(x1,...,xn)=0, the number of zeros of grad(p) might be different from that of grad(q). This implies, in particular, that, although the fibers p=0 and q=0 are isomorphic, there are some other fibers p=c and q=c which are not. We construct examples like this for any n≥2. © 2001 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/75413
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.accessioned2010-09-06T07:10:53Z-
dc.date.available2010-09-06T07:10:53Z-
dc.date.issued2001en_HK
dc.identifier.citationJournal Of Algebra, 2001, v. 239 n. 1, p. 161-173en_HK
dc.identifier.issn0021-8693en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75413-
dc.description.abstractIn this paper, we address the following two general problems: given two algebraic varieties in Cn, find out whether or not they are (1) isomorphic and (2) equivalent under an automorphism of Cn. Although a complete solution of either of those problems is out of the question at this time, we give here some handy and useful invariants of isomorphic as well as of equivalent varieties. Furthermore, and more importantly, we give a universal procedure for obtaining all possible algebraic varieties isomorphic to a given one and use it to construct numerous examples of isomorphic but inequivalent algebraic varieties in Cn. Among other things, we establish the following interesting fact: for isomorphic hypersurfaces p(x1,...,xn)=0 and q(x1,...,xn)=0, the number of zeros of grad(p) might be different from that of grad(q). This implies, in particular, that, although the fibers p=0 and q=0 are isomorphic, there are some other fibers p=c and q=c which are not. We construct examples like this for any n≥2. © 2001 Academic Press.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.titleEmbeddings of hypersurfaces in affine spacesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-8693&volume=239 no1&spage=161&epage=173&date=2001&atitle=Embeddings+of+hypersurfaces+in+affine+spacesen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1006/jabr.2000.8677en_HK
dc.identifier.scopuseid_2-s2.0-0035343386en_HK
dc.identifier.hkuros63201en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0035343386&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume239en_HK
dc.identifier.issue1en_HK
dc.identifier.spage161en_HK
dc.identifier.epage173en_HK
dc.identifier.isiWOS:000168456600008-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridShpilrain, V=6603904879en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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