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On the Algebraic Dimension of Twistor Spaces over the Connected Sum of Four Complex Projective Planes

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Abstract

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.

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Kreuβler, B. On the Algebraic Dimension of Twistor Spaces over the Connected Sum of Four Complex Projective Planes. Geometriae Dedicata 71, 263–285 (1998). https://doi.org/10.1023/A:1005038726026

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