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Article: Deformation rigidity of the rational homogeneous space associated to a long simple root

TitleDeformation rigidity of the rational homogeneous space associated to a long simple root
Authors
KeywordsMathematics
Issue Date2002
PublisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/ansens
Citation
Annales Scientifiques De L'ecole Normale Superieure, 2002, v. 35 n. 2, p. 173-184 How to Cite?
AbstractAs a continuation of our previous works we study the conjecture on the rigidity under Kähler deformation of the complex structure of rational homogeneous spaces G / P of Picard number 1, confirming its validity whenever G / P is associated to a long simple root. For these rational homogeneous spaces the minimal G-invariant holomorphic distribution D is spanned by varieties of minimal rational tangents, and, excepting the symmetric and the contact cases, the complex structure of G / P is completely determined by the nilpotent symbol algebra of the weak derived differential system of D. The problem is reduced, in a sense, to the invariance of this nilpotent symbol algebra under Kähler deformation. In our earlier works in relation to the question of the integrability of distributions spanned by varieties of minimal rational tangents we have established identities on Lie brackets using integral surfaces arising from pencils of rational curves. In the case on hand, at a point oε G / P we prove that the nilpotent symbol algebra at o is nothing other than the universal Lie algebra generated by Do subject to these identities on Lie brackets, by verifying that they correspond to finiteness condition in the Serre presentation of the simple Lie algebra G. © 2002 Éditions scientifiques et médicales Elsevier SAS.
Persistent Identifierhttp://hdl.handle.net/10722/48606
ISSN
2015 Impact Factor: 1.83
2015 SCImago Journal Rankings: 3.966
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorHwang, JMen_HK
dc.contributor.authorMok, Nen_HK
dc.date.accessioned2008-05-22T04:18:47Z-
dc.date.available2008-05-22T04:18:47Z-
dc.date.issued2002en_HK
dc.identifier.citationAnnales Scientifiques De L'ecole Normale Superieure, 2002, v. 35 n. 2, p. 173-184en_HK
dc.identifier.issn0012-9593en_HK
dc.identifier.urihttp://hdl.handle.net/10722/48606-
dc.description.abstractAs a continuation of our previous works we study the conjecture on the rigidity under Kähler deformation of the complex structure of rational homogeneous spaces G / P of Picard number 1, confirming its validity whenever G / P is associated to a long simple root. For these rational homogeneous spaces the minimal G-invariant holomorphic distribution D is spanned by varieties of minimal rational tangents, and, excepting the symmetric and the contact cases, the complex structure of G / P is completely determined by the nilpotent symbol algebra of the weak derived differential system of D. The problem is reduced, in a sense, to the invariance of this nilpotent symbol algebra under Kähler deformation. In our earlier works in relation to the question of the integrability of distributions spanned by varieties of minimal rational tangents we have established identities on Lie brackets using integral surfaces arising from pencils of rational curves. In the case on hand, at a point oε G / P we prove that the nilpotent symbol algebra at o is nothing other than the universal Lie algebra generated by Do subject to these identities on Lie brackets, by verifying that they correspond to finiteness condition in the Serre presentation of the simple Lie algebra G. © 2002 Éditions scientifiques et médicales Elsevier SAS.en_HK
dc.format.extent43190256 bytes-
dc.format.extent160101 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/pdf-
dc.languageengen_HK
dc.languagefreen_HK
dc.publisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/ansensen_HK
dc.relation.ispartofAnnales Scientifiques de l'Ecole Normale Superieureen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsAnnales Scientifiques de l'Ecole Normale Superieure. Copyright © Elsevier France, Editions Scientifiques et Medicales.en_HK
dc.subjectMathematicsen_HK
dc.titleDeformation rigidity of the rational homogeneous space associated to a long simple rooten_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0012-9593&volume=35&issue=2&spage=173&epage=184&date=2002&atitle=Deformation+rigidity+of+the+rational+homogeneous+space+associated+to+a+long+rooten_HK
dc.identifier.emailMok, N:nmok@hkucc.hku.hken_HK
dc.identifier.authorityMok, N=rp00763en_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1016/S0012-9593(02)01087-Xen_HK
dc.identifier.scopuseid_2-s2.0-0036239335en_HK
dc.identifier.hkuros66705-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0036239335&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume35en_HK
dc.identifier.issue2en_HK
dc.identifier.spage173en_HK
dc.identifier.epage184en_HK
dc.identifier.isiWOS:000176408000002-
dc.publisher.placeFranceen_HK
dc.identifier.scopusauthoridHwang, JM=7403895554en_HK
dc.identifier.scopusauthoridMok, N=7004348032en_HK

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