ar X iv : m at h / 04 06 10 9 v 1 [ m at h . C V ] 7 J un 2 00 4 VALUATIONS AND MULTIPLIER IDEALS

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with of ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the “openness conjecture” by Demailly and Kollár. Our technique also enables us to give new proofs of two recent results: one on the structure of the set of complex singularity exponents for holomorphic functions; the other by Lipman and Watanabe on the realization of ideals as multiplier ideals.