Abstract
In this note, we study validity of the original Briançon-Skoda theorem for analytic local rings. By introducing a new concept of multiplier ideal sheaves associated to plurisubharmonic functions on any (reduced) complex space of pure dimension, we establish the original Briançon-Skoda theorem for normal weakly rational singularities (not essentially of finite type over C and Cohen-Macaulay). Moreover, we also characterize two dimensional rational singularities by the original Briançon-Skoda theorem.
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