Multiplier ideals in two-dimensional local rings with rational singularities
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The 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.
CitationAlberich, M., Alvarez, J., Dachs, F. Multiplier ideals in two-dimensional local rings with rational singularities. "Michigan mathematical journal", 2016, vol. 65, núm. 2, p. 287-320.
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