dc.contributor.creator Kreussler, Bernd dc.date.accessioned 2018-10-05T11:09:22Z dc.date.available 2018-10-05T11:09:22Z dc.date.issued 1999 dc.identifier.citation Kreussler, B. (1999) Twistor Spaces With a Pencil of Fundamental Divisors. Documenta Mathematica 4(1). pp. 127-166. ISSN: 1431-0643. en_US dc.identifier.issn 1431-0643 dc.identifier.uri http://hdl.handle.net/10395/2224 dc.description Twistor spaces with a pencil of fundamental divisors en_US dc.description.abstract In 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 en_US rational non-real curve C with C:(-1/2K) = 2-n. dc.language.iso eng en_US dc.publisher Documenta Mathematica en_US dc.relation.ispartofseries 4;1 dc.rights.uri https://www.math.uni-bielefeld.de/documenta/vol-04/05.pdf en_US dc.subject Moishezon manifold en_US dc.subject Algebraic dimension en_US dc.subject Self-dual en_US dc.subject Twistor space en_US dc.title Twistor spaces with a pencil of fundamental divisors en_US dc.type Article en_US dc.type.supercollection all_mic_research en_US dc.type.supercollection mic_published_reviewed en_US dc.description.version Yes en_US
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