MOISHEZON TWISTOR SPACES WITHOUT EFFECTIVE DIVISORS OF DEGREE ONE

We study simply connected compact twister spaces Z of positive type. A ssuming that the fundamental linear system \-1/2 K\ is at lease a penc il, we prove the following theorem: the existence of an irreducible ra tional curve C subset of Z, which is invariant under the real structur e of Z and has the property C.(-1/2 K) < 0, implies that the twistor s pace is Moishezon does not contain effective divisors of degree one. F urthermore, we prove the existence of such twister spaces with arbitra ry Picard number rho(Z) greater than or equal to 5. These are the firs t examples of Moishezon twister spaces without effective divisors of d egree one.