On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes

Details On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes

1996-07-04

arxiv.org/abs/alg-geom/9607007v1

Mathematics

Algebraic Geometry

23 pages LaTeX 2e

Scientific paper

We study the algebraic dimension of twistor spaces of positive type over $4\bbfP^2$. We show that such a twistor space is Moishezon if and only if its anticanonical 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 $|{-1/2}K|$. This implies, for example, $\dim|{-1/2}K|\leq a(Z)$. We characterize those twistor spaces over $4\bbfP^2$, which contain a pencil of divisors of degree one by the property $\dim|{-1/2}K| = 3$.

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