DC Field | Value | Language |
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dc.contributor.author | Jeong, Yewon | ko |
dc.date.accessioned | 2018-12-20T06:51:58Z | - |
dc.date.available | 2018-12-20T06:51:58Z | - |
dc.date.created | 2018-12-12 | - |
dc.date.created | 2018-12-12 | - |
dc.date.issued | 2018-10 | - |
dc.identifier.citation | MATHEMATISCHE ANNALEN, v.372, no.1-2, pp.1 - 54 | - |
dc.identifier.issn | 0025-5831 | - |
dc.identifier.uri | http://hdl.handle.net/10203/248299 | - |
dc.description.abstract | Griffiths and Harris (Ann Sci Ec Norm Super 12: 355-432, 1979) asked whether a projective complex submanifold of codimension two is determined by the moduli of its second fundamental forms. More precisely, given a nonsingular subvariety Xn. Pn+ 2, the second fundamental form IIX, x at a point x. X is a pencil of quadrics on Tx (X), defining a rational map mu X from X to a suitable moduli space of pencils of quadrics on a complex vector space of dimension n. The question raised by Griffiths and Harris was whether the image of mu X determines X. We study this question when Xn. Pn+ 2 is a nonsingular intersection of two quadric hypersurfaces of dimension n > 4. In this case, the second fundamental form IIX, x at a general point x. X is a nonsingular pencil of quadrics. Firstly, we prove that the moduli map mu X is dominant over the moduli of nonsingular pencils of quadrics. This gives a negative answer to Griffiths-Harris's question. To remedy the situation, we consider a refined version mu X of the moduli map mu X, which takes into account the infinitesimal information of mu X. Our main result is an affirmative answer in terms of the refined moduli map: we prove that the image of mu X determines X, among nonsingular intersections of two quadrics. | - |
dc.language | English | - |
dc.publisher | SPRINGER HEIDELBERG | - |
dc.title | Moduli map of second fundamental forms on a nonsingular intersection of two quadrics | - |
dc.type | Article | - |
dc.identifier.wosid | 000445199600001 | - |
dc.identifier.scopusid | 2-s2.0-85019753542 | - |
dc.type.rims | ART | - |
dc.citation.volume | 372 | - |
dc.citation.issue | 1-2 | - |
dc.citation.beginningpage | 1 | - |
dc.citation.endingpage | 54 | - |
dc.citation.publicationname | MATHEMATISCHE ANNALEN | - |
dc.identifier.doi | 10.1007/s00208-017-1556-9 | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
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