Multiplier ideals in two-dimensional local rings with rational singularities

arXiv:1412.3605v2The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next jumping number. This leads to an algorithm to compute sequentially the jumping numbers and the whole chain of multiplier ideals in any desired range. As a consequence of our method we develop the notion of jumping divisor that allows to describe the jump between two consecutive multiplier ideals. In particular we find a unique minimal jumping divisor that is studied extensively.All three authors were partially supported by Generalitat de Catalunya 2014 SGR-634 project and Spanish Ministerio de Economía y Competitividad MTM2012-38122-03-01/FEDER. FDC is also supported by the KU Leuven grant OT/11/069.Peer Reviewe