On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes
Abstract
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 $\dim{1/2}K = 3$.
 Publication:

arXiv eprints
 Pub Date:
 July 1996
 arXiv:
 arXiv:alggeom/9607007
 Bibcode:
 1996alg.geom..7007K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry;
 32L25
 EPrint:
 23 pages LaTeX 2e