When is a complete ideal in a rational surface singularity a multiplier ideal?

This is an extended abstract with some of the results that will appear in the forthcoming paper [1] in which we characterize when a given complete ideal in a two-dimensional local ring with a rational singularity can be realized as a multiplier ideal.All three authors are partially supported by Spanish Ministerio de Ciencia y Educaciòn PID2019-103849GB-I00. VGA is partially supported by ERC StG 279723 “Arithmetic of algebraic surfaces" (SURFARI). MAC and JAM are also supported by Generalitat de Catalunya SGR2017-932 project and they are with the Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech) and the Barcelona Graduate School of Mathematics (BGSMath). MAC is also with the Institut de Robòtica i Informàtica Industrial (CSIC-UPC). VGA is also a member of the Riemann Center for Geometry and Physics.Peer ReviewedPostprint (published version