On the diffeomorphism groups of rational and ruled 4-manifolds

Let A(M) be the automorphism group of the middle homology of a smooth 4-manifold M and D(M) be the subgroup induced by diffeomorphisms of M. In this paper we give explicit generators of D(M) for rational and ruled 4-manifolds. We also prove the uniqueness of reduced forms for classes with minimal genus 0 and non-negative square.