On the (?1)-curve conjecture of friedman and morgan

Summary We will prove that every differentiably embedded sphere with self-intersection –1 in a simply connected algebraic surface withp _g >0 is homologous to an algebraic class. If the surface has a minimal model with Picard number 1 or |K _min| contains a smooth curve, and eitherp _g orK _min ² is even, then every such sphere is homologous to a (–1)-curve, as conjectured by Friedman and Morgan.Oblatum 15-IV-1993Supported by Nederlandse organisatie voor wetenschappelijk onderzoek NWO, stipend 04-63.