Geometric properties of projective manifolds of small degree

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dc.contributor.authorKwak, Sijongko
dc.contributor.authorPark, Jinhyungko
dc.date.accessioned2016-09-07T01:08:26Z-
dc.date.available2016-09-07T01:08:26Z-
dc.date.created2016-08-08-
dc.date.created2016-08-08-
dc.date.issued2016-03-
dc.identifier.citationMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v.160, no.2, pp.257 - 277-
dc.identifier.issn0305-0041-
dc.identifier.urihttp://hdl.handle.net/10203/212500-
dc.description.abstractThe aim of this paper is to study geometric properties of non-degenerate smooth projective varieties of small degree from a birational point of view. First, using the positivity property of double point divisors and the adjunction mappings, we classify smooth projective varieties in P-r of degree d <= r + 2, and consequently, we show that such varieties are simply connected and rationally connected except in a few cases. This is a generalisation of P. Ionescu's work. We also show the finite generation of Cox rings of smooth projective varieties in P-r of degree d <= r with counterexamples for d = r + 1, r + 2. On the other hand, we prove that a non-uniruled smooth projective variety in P-r of dimension n and degree d <= n(r - n) + 2 is Calabi-Yau, and give an example that shows this bound is also sharp-
dc.languageEnglish-
dc.publisherCAMBRIDGE UNIV PRESS-
dc.subjectMORI DREAM SPACES-
dc.subjectVECTOR-BUNDLES-
dc.subjectMINIMAL MODELS-
dc.subjectGREATER-THAN-
dc.subjectFANO 3-FOLDS-
dc.subjectVARIETIES-
dc.subjectSURFACES-
dc.subjectCLASSIFICATION-
dc.subjectCODIMENSION-
dc.subjectCONJECTURE-
dc.titleGeometric properties of projective manifolds of small degree-
dc.typeArticle-
dc.identifier.wosid000379502100004-
dc.identifier.scopusid2-s2.0-84958119924-
dc.type.rimsART-
dc.citation.volume160-
dc.citation.issue2-
dc.citation.beginningpage257-
dc.citation.endingpage277-
dc.citation.publicationnameMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-
dc.identifier.doi10.1017/S0305004115000663-
dc.contributor.localauthorKwak, Sijong-
dc.type.journalArticleArticle-
dc.subject.keywordPlusMORI DREAM SPACES-
dc.subject.keywordPlusVECTOR-BUNDLES-
dc.subject.keywordPlusMINIMAL MODELS-
dc.subject.keywordPlusGREATER-THAN-
dc.subject.keywordPlusFANO 3-FOLDS-
dc.subject.keywordPlusVARIETIES-
dc.subject.keywordPlusSURFACES-
dc.subject.keywordPlusCLASSIFICATION-
dc.subject.keywordPlusCODIMENSION-
dc.subject.keywordPlusCONJECTURE-
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