Adjunction inequality for a simple J-holomorphic sphere ($c_1(A)\le A^2+2$)

The singular-curve adjunction formula in a symplectic manifold of real dimension four gives $c_1(A)=A^2+2-2\delta$ for a simple J-holomorphic sphere, with a nonnegative singularity count $\delta$. Hence the displayed inequality holds. This is the version needed when the sphere need not be embedded.