Embeddings of surfaces in 4-manifolds. II (Q1200046)

[Part I is reviewed above (see Zbl 0764.57021).] The author applies Donaldson's result on the nonexistence of certain unimodular forms as intersection forms of smooth 4-manifolds to the problem of representing 2-dimensional homology classes of smooth simply connected 4-manifolds by embedded 2-spheres. He obtains a new necessary condition for the connected sums \(-CP^ 2\# nCP^ 2\) and primitive homology classes \(x\) with \(x^ 2=0\). This leads to a complete answer for such classes and \(n<10\).