Abstract
We characterize ideals whose adjoints are determined by their Rees valuations. We generalize the notion of a regular system of parameters, and prove that for ideals generated by monomials in such elements, the integral closure and adjoints are generated by monomi- als. We prove that the adjoints of such ideals and of all ideals in two- dimensional regular local rings are determined by their Rees valuations. We prove special cases of subadditivity of adjoints. Adjoint ideals and multiplier ideals have recently emerged as a fundamental tool in commutative algebra and algebraic geometry. In characteristic 0 they may be defined using resolution of singularities. In all characteristics, even mixed, Lipman gave the following definition:
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