In this paper simply connected twistor spaces Z containing a pencil of fundamental divisors are studied. The Riemannian base for such spaces is diieomorphic to the connected sum nC P 2. We obtain for n 5 a complete description of the set of curves intersecting the fundamental line bundle K 1 2 negatively. For this purpose we introduce a combinatorial structure, called blow-up graph. We show that for generic S 2j 1 2