Bounds on genus and configurations of embedded surfaces in 4‐manifolds

For several embedded surfaces with zero self‐intersection number in 4‐manifolds, we show that an adjunction‐type genus bound holds for at least one of the surfaces under certain conditions. For example, we derive certain adjunction inequalities for surfaces embedded in mCP2#n(−CP2)(m,n⩾2) . The proofs of these results are given by studying a family of the Seiberg–Witten equations.