On tori embedded in four-manifolds (Q688604)

Let \(M\) be a smooth, closed simply connected 4-manifold with \(b^ +_ 2(M) > 1\) odd. We prove that the existence of a smoothly embedded 2-torus \(T \hookrightarrow M\) with self-intersection \(+1\) implies that the generalized Donaldson polynomials of \(M\) vanish on the orthogonal complement of the homology class represented by \(T\). We show how this implies that there are no such tori inside a smooth simply connected complex surface with geometric genus greater than zero whose minimal model is either elliptic or a complete intersection.