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dc.contributor.creatorKreussler, Bernd
dc.date.accessioned2018-10-05T11:09:22Z
dc.date.available2018-10-05T11:09:22Z
dc.date.issued1999
dc.identifier.citationKreussler, B. (1999) Twistor Spaces With a Pencil of Fundamental Divisors. Documenta Mathematica 4(1). pp. 127-166. ISSN: 1431-0643.en_US
dc.identifier.issn1431-0643
dc.identifier.urihttp://hdl.handle.net/10395/2224
dc.descriptionTwistor spaces with a pencil of fundamental divisorsen_US
dc.description.abstractIn this paper simply connected twistor spaces Z containing a pencil of fundamental divisors are studied. The Riemannian base for such spaces is diffeomorphic to the connected sum nCP2 . We obtain for n 5 a complete description of the set of curves intersecting the fundamental line bundle K-1/2 negatively. For this purpose we introduce a combinatorial structure, called blow-up graph. We show that for generic S 2j-1/2K j the algebraic dimension can be computed by the formula a(Z) = 1 + K-1(S). A detailed study of the anti Kodaira dimension K-1(S) of rational surfaces permits to read o the algebraic dimension from the blow-up graphs. This gives a characterisation of Moishezon twistor spaces by the structure of the corresponding blow-up graphs. We study the behaviour of these graphs under small deformations. The results are applied to prove the main existence result, which states that every blow-up graph belongs to a fundamental divisor of a twistor space. We show, furthermore, that a twistor space with dim -1/2K = 3 is a LeBrun space [LeB2]. We characterise such spaces also by the property to contain a smooth rational non-real curve C with C:(-1/2K) = 2-n.en_US
dc.language.isoengen_US
dc.publisherDocumenta Mathematicaen_US
dc.relation.ispartofseries4;1
dc.rights.urihttps://www.math.uni-bielefeld.de/documenta/vol-04/05.pdfen_US
dc.subjectMoishezon manifolden_US
dc.subjectAlgebraic dimensionen_US
dc.subjectSelf-dualen_US
dc.subjectTwistor spaceen_US
dc.titleTwistor spaces with a pencil of fundamental divisorsen_US
dc.typeArticleen_US
dc.type.supercollectionall_mic_researchen_US
dc.type.supercollectionmic_published_revieweden_US
dc.description.versionYesen_US


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