Geometriae Dedicata

, Volume 71, Issue 3, pp 263–285

Regular Paper

  • B. Kreuβler


We study the algebraic dimension of twistor spaces of positive type over 4CP2. We show that such a twistor space is Moishezon if and only if its anti-canonical class is not nef. More precisely, we show the equivalence of being Moishezon with the existence of a smooth rational curve having negative intersection number with the anticanonical class. Furthermore, we give precise information on the dimension and base locus of the fundamental linear system |-1/2|. This implies, for example, dim|-1/2K| ≤ a(Z). We characterize those twistor spaces over 4CP2, which contain a pencil of divisors of degree one by the property dim|-1/2K| = 3.

twistor space self-dual manifold algebraic dimension rational surface. 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • B. Kreuβler
    • 1
  1. 1.FB MathematikUniversität KaiserslautgernKaiserlauternGermany; e-mail

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