We analyze the fine structure of Clark measures and isometries associated with two-variable rational inner functions on bidisk. In degree (n,1) case, we give a complete description supports weights for both generic exceptional measures, characterize when embedding operators are unitary, formula those operators. also highlight connections between our results Agler decompositions study extreme po...

We prove the existence of (non compact) complex surfaces with a smooth rational curve embedded such that there does not exist any formal singular foliation along curve. In particular, at arbitrary small neighborhood curve, meromorphic function is constant. This implies Picard group countably generated.