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복소기하학연구단
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Characterizing symplectic Grassmannians by varieties of minimal rational tangents

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dc.contributor.authorJun-Muk Hwang-
dc.contributor.authorQifeng Li-
dc.date.accessioned2021-12-22T00:30:01Z-
dc.date.available2021-12-22T00:30:01Z-
dc.date.created2021-11-01-
dc.date.issued2021-10-
dc.identifier.issn0022-040X-
dc.identifier.urihttps://pr.ibs.re.kr/handle/8788114/10912-
dc.description.abstract© 2021 International Press of Boston, Inc.. All rights reserved.We show that if the variety of minimal rational tangents (VMRT) of a uniruled projective manifold at a general point is projectively equivalent to that of a symplectic or an odd-symplectic Grassmannian, the germ of a general minimal rational curve is biholomorphic to the germ of a general line in a presymplectic Grassmannian. As an application, we characterize symplectic and odd-symplectic Grassmannians, among Fano manifolds of Picard number 1, by their VMRT at a general point and prove their rigidity under global Kähler deformation. Analogous results for G/P associated with a long root were obtained by Mok and Hong-Hwang a decade ago by using Tanaka theory for parabolic geometries. When G/P is associated with a short root, for which symplectic Grassmannians are most prominent examples, the associated local differential geometric structure is no longer a parabolic geometry and standard machinery of Tanaka theory cannot be applied because of several degenerate features. To overcome the difficulty, we show that Tanaka's method can be generalized to a setting much broader than parabolic geometries, by assuming a vanishing condition that certain vector bundles arising from Spencer complexes have no nonzero sections. In our application of this method to the characterization of symplectic (or odd-symplectic) Grassmannians, this vanishing condition is checked by exploiting geometry of minimal rational curves.-
dc.language영어-
dc.publisherInternational Press, Inc.-
dc.titleCharacterizing symplectic Grassmannians by varieties of minimal rational tangents-
dc.typeArticle-
dc.type.rimsART-
dc.identifier.wosid000702468500004-
dc.identifier.scopusid2-s2.0-85115909839-
dc.identifier.rimsid76604-
dc.contributor.affiliatedAuthorJun-Muk Hwang-
dc.contributor.affiliatedAuthorQifeng Li-
dc.identifier.doi10.4310/jdg/1632506422-
dc.identifier.bibliographicCitationJournal of Differential Geometry, v.119, no.2, pp.309 - 381-
dc.relation.isPartOfJournal of Differential Geometry-
dc.citation.titleJournal of Differential Geometry-
dc.citation.volume119-
dc.citation.number2-
dc.citation.startPage309-
dc.citation.endPage381-
dc.type.docTypeArticle-
dc.description.journalClass1-
dc.description.journalClass1-
dc.description.isOpenAccessN-
dc.description.journalRegisteredClassscie-
dc.description.journalRegisteredClassscopus-
dc.relation.journalResearchAreaMathematics-
dc.relation.journalWebOfScienceCategoryMathematics-
dc.subject.keywordPlusGEOMETRIC STRUCTURES-
dc.subject.keywordPlusPROJECTIVE VARIETIES-
dc.subject.keywordPlusMANIFOLDS-
dc.subject.keywordAuthorCartan connections-
dc.subject.keywordAuthorMinimal rational curves-
dc.subject.keywordAuthorSymplectic Grassmannians-
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Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
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